[oddsock]

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This sort of problem continues haunting me.

Should the K or Q on board change the probability of your opponents hole cards? I think to figure out the probability of his holding K or Q, all 8 cards are counted. His cards are dealt before the flop/turn.

Same as the well-known car-sheep problem? Behind three doors, one car and two sheep. You pick up one door and then shown one other door which is a sheep. Should you change to the third door to get a better chance of car or it makes no difference?

Back to poker, if the flop are 3 spades, and you want to calculate the prob that he made flush. The Bayesian prior should be 13C2 / 52C2, not 10C2 / 52C2 right?

To make things worse, I think your hole cards should count. Ie, hero's pair of ten would increase the probability that his opponent gets Q or K.

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Problem is that the car/sheep situation is purely random - there are no other factors in place that can help you. (Solution by the way is to ALWAYS change the original choice!).

If you have no read on your opponent whatsoever then a K or Q appearing on the turn will reduce the chances of the opponent having a K or Q in his hand from a purely mathematical point of view in the same way that a one-suit flop would mathematically reduce the chances of an opponent having the same suit hole cards. That does not mean they won't have the cards that are mathematically less probable, so as a poker player you need to use the other tools at your disposal to make as accurate read as possible.