At what point is a question concerning probability abstract enough that it is more appropriate on the math stackexchange instead of crossvalidated?
I don't think there's necessarily a point at which this occurs. Probability is on topic and theoretical questions are on topic.
Since it will almost certainly be on topic at either, it's a matter of judgement which you choose - there's no universally correct answer, but your aim is to get an answer you can use. Some questions will get a better answer here, some there; some will get similar answers either way. Indeed a number of users spend time on both sites, so they may well post identical answers to what they would have posted at the other.
So you simply pick whichever site you think will get you the best answers for what you're seeking (and if you think you picked wrong after you post, flag and ask it to be migrated).
If it's getting up around research-level, you might also consider whether mathoverflow might be the best place (but pay attention to the somewhat different way their posts are tagged than the other two sites).