A cute probability intuition test:
Let $f$ be the probability of being dealt a full house in a five-card poker hand, from a randomly shuffled standard deck. ($f \approx 0.001468$).
Now look at the case of two players being dealt hands, and player one shows that she has a flush. Now what is the probability $f_2$ that the five cards dealt to player 2 is a full house?
It seems clear that we will have $f_2 < f$ because if one player has a full house it must be a tiny bit more likely that the other has pairs and other clumps of the same rank, and a flush has none of those. But to test your intuition, how small is that effect?
Is $f_2$ more than 99% of $f$? More than 95%? More than 90%? or less than 90%?
EDIT I had written $h$ for "house" in the first sentence. Then I used $f$ for "full" later.