Unless the PCs try to hide the fact that they are now seeing the sniper, then I think it will be clear for the sniper that his attempt to hide failed.
Maybe allow a sense motive check for her to notice. And if your PCs make use of meta knowledge like that then I'd say that it's not unfair for a skilled NPC to do the same (though ideally neither should, I would be happy to let the PCs do that sense motive check if they don't use meta).
My NPCs know the same stuff as my PCs. If my NPC rolls a 17 to hit in combat and fails to hit, he knows the PC has very high armor class. If I don't want my PCs to know if they did a good job on a disguise or perception check, I'll roll it in secret for them.
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I'd say that if you spot a sniper and want to keep an eye on him so he doesn't sneak attack you, you'll be glancing in his direction from time to time. You could try to be subtle about it, because you don't want to let him know you spotted it; that sounds like a good moment for opposed checks. Probably Bluff vs. Sense Motive.
If the creature using Stealth attacked from hiding during a surprise round, then this must be resolved as its own Perception check to prevent being surprised, but not necessarily to observe the creature attacking. A creature prevented from being surprised and to observe their attacker are two separate checks, made at the same time as the creature breaks Stealth (with an attack, opposed by the creature's Stealth check to remain hidden upon an approach, to determine surprise) and then re-enters Stealth (the creature sniped/attacked in melee, then is able to re-enter Stealth either as a move action [Sniping] or as part of movement [Any attack other than ranged attacks], to determine a successful attempt at hiding).
If a creature makes their Stealth check as part of re-entering stealth, they were not observed at any point by the perceiving creature until the the attack, even if they were not surprised. Even a surprised creature can attempt to perceive their attacker as they enter stealth, but this does not prevent the creature from being surprised.
To find a creature currently in Stealth that you failed to observe as they entered Stealth, you must use a move action to locate the creature. If your Perception check beats the creature's Stealth check, then you know the location of the creature, and can perceive them unless some other effect prevents you from observing them (like invisibility).
You can passively make Perception checks, but you are never aware that you are making these checks at any point. This is to simulate your brain's natural ability to block out and give importance to particular stimuli, and your Perception being a more fine-tuned capability of determining when something is or is not important stimuli.
When you successfully perceive or know the location of a creature in Stealth, this does not mean other creatures can perceive the creature as well. Successfully determining a hidden creature's location does not also confer this to other creatures. They must make their own actions or Perception attempts to perceive the hidden creature. However, informing other creatures of a hidden creature's position entitles them to a reactive Perception check to locate the hidden creature and possibly allow them to perceive the hidden creature or determine its location.
Determining a creature's ability to perceive a hidden creature depends on functional stimulus. To be allowed to Stealth, a creature must have cover or concealment of any kind. Total concealment or total cover functionally prevent a creature from being observed visually, as they prevent a creature from having line of sight or line of effect respectively. Treat this as being invisible to an observer unable to perceive them through other senses.
If a creature is not moving, hidden within darkness, while a human without light to shine into the darkness is trying to perceive them, then the hidden creature is effectively invisible. In this situation, the human must beat a Perception DC of 20+the creature's Stealth score to be able to determine their location. This assumes the human knows that there is a hidden creature within the darkness. Otherwise, the human is not entitled to a reactive Perception check, as the creature is making no noise from moving, and is not perceivable by the human's senses.
If a creature is invisible (as the spell invisibility), then it is granted this benefit at all times on visual based Perception checks. An invisible creature cannot be perceived visually by any creature unable to see invisible creatures, and so these creatures are never entitled to a reactive Perception check due to visual stimulus.
If, in either case, the creature moves, and that movement is not muffled (such as from the silence spell), then a creature is entitled to a Perception check of a DC set by the moving hidden creature's Stealth check. This allows a creature to determine the invisible creature's location, but not to perceive them. This is because sound is a separate stimuli to vision. And so long as a creature is capable of hearing, they are able to make audio-based Perception checks.
I view it as how in real life you know how good you are doing at things most of the time. Examples
Taking a test. Afterwards you know about how much of the information you knew
Cooking. Almost everyone takes a few tastes to see how things are going along or has gone when your finished
Sneaking. You can hear yourself and you also know how much of yourself was visible for however long
That said there are times where you really don't. IE perception checks. Seems like it should be your judgement call as to whether or not they can realize this on a case by case basis.
My personal opinion is that you have a vague idea of how well you perform an action. Even if real life you tend to have an idea of how well you did something. As an example, ever went bowling. You release that ball you already have a good idea of how well your going to connect with those pins.
I think this situation could be like that. You know that you did decently, but with the difficulty of hiding after shooting someone (the sniping penalty) you know you didn't do great. It's reasonable to consider spending your next turn to hide again.
Of course that's assuming the PCs don't just try to kill you outright on their turn.
As far as having some people make the perception check and some fail and being to discern which is which....maybe. The idea of sense motive vs bluff seems reasonable, but it's not rules. Still this is the closest approximation you would have.
I think the important case where an NPC (or a PC) should not know how well they rolled is when making sense motive checks. Rolling "to see if they're lying" and then knowing you rolled poorly, so you conclude that they're probably lying, is approaching that line of "too megatamey". Fair to still be suspicious because of who they are or the implausibility of the story, but you shouldn't be suspicious because you know how well or poorly you rolled.
I agree Possible Cabbage, reactionary skills you probably shouldn't have an idea of how well you performed such as perception or sense motive. Anything that involves you physically doing something you probably have a vague idea of how you did.
My NPCs don't know, they base their decisions based on what happens.
My players take full advantage of such meta game knowledge, but that disparity doesn't bother me. (In cases like sense motive, we generally have the DM roll - we don't find the low rolls problematic but rather the high rolls with a "telling the truth" result).
My personal opinion is that you have a vague idea of how well you perform an action. Even if real life you tend to have an idea of how well you did something. As an example, ever went bowling. You release that ball you already have a good idea of how well your going to connect with those pins.True, but sometimes that ball you thought was great gives you the 7-10 split 'cuz you hit 1/4" too much on the head pin.
Other times, I've let loose a ball where I almost fell on my butt, but crazy garbage pin-action caused a strike.
I said a vague idea, not perfect intuition.