Grease near ledges or pits

[Bezzlemint]

I know the rules on grease as regards the reflex save, the slower speed, and even standing. My question is a small but important detail about the falling bit. Some scenarios have an NPC grease a hazard like a bridge or a bridge with caltrops already on it.

Now according to the rules, fail your save - fall prone. But it appears that you always fall prone in your own square. So the ledge isn't an additional threat? Are there rules that might imply falling in a random direction other than straight down? What if your standing on a grease bridge and a goblin with a horse clopper is trying to trip you? Trip still has you fall straight down so the bridge poses no additional threat. Do the caltrops cause greater damage when you fall in them?

[Nixitur]

As far as I can see, RAW, the answer to all those questions is no. I'm not even seeing any rules for falling off rooftops you're running on or in the description for Acrobatics. There is nothing in the rules that implies that you ever "slide" into a different square just by yourself, not even when moving on ice. As the rules are written, even on a slanted roof in a cold winter with grease in your square, you never run the risk of involuntarily sliding into another square or off the roof.

[Rub-Eta]

Falling and falling prone are not the same thing. Falling prone means that you drop to the ground and gain the prone condition. Falling of a ledge, on the other hand, does not necessarily mean that you fall prone.

A slippery bridge or a slated roof during a cold winter is probably a hazard that doesn't drop you prone, but instead makes you plummet towards a very hard and sudden stop.

Adding a spell like grease to a narrow ledge increases the narrow ledge's DC by +5 (assuming that it's as slippery as ice), in addition to the spell's normal effect.

[Nixitur]

Hmm, there is the section on "Crossing Narrow Surfaces/Uneven Ground" under Acrobatics. I always thought this referred to walking across a thin beam, but I suppose it could also refer to dangerous ledges. And it does refer to "falling" and "being knocked prone" as different outcomes.
Although it's a bit of a stretch to consider a big bridge that just happens to have Grease along its edges as either uneven ground or a narrow surface.

[Felix Danger]

Yes the narrow surface rules for a bridge 3 feet wide offer 0 chance of failure. Adding severely slippery and heavily obstructed would raise that to 10. But even then, the rules are vague and say "avoid falling or being knocked prone" but not which. I feel like the scenario as written wants a chance for the players to fall into the water but there's no rules to make it happen.