Using Conditional Probability in Poker

[napawino]

Ok, obviously the Monty Hall problem has been discussed on here before & while I'm impressed that more 2+2ers get this right than my co-workers & professional friends, I can't say that I'm surprised. Now, how can I use the idea of conditional probability in poker?

An obvious example is where I have good notes on people & I KNOW they will play ANY Ace or King from ANY position. (& I have this note on LOTS of low-limit online players.) If I see three of these players fold & I look down to see AK, haven't my odds of flopping an Ace or a King just gone up by around 5% from the standard odds? And if I miss on the flop, hasn't my 1/6.8 gone down to 1/5.8 of hitting an Ace or a King on the turn?

Are there other examples that could be used? (If Doyle folds or plays, do you know that your TT or 22 is a better or worse hand?) (Of course I know that he doesn't ALWAYS play this hand, but I hope you get the point.) Is there other information that you can use to adjust the standard probabilities & is the difference worth the effort?

[SomethingClever]

I think it's useful to at least think about stuff like this. I play low-limit only, and it is remarkable how many players at those levels are of the "any ace, any king" variety.