The probability of winning the lottery if you're a cheater is high, but the probability of being a cheater if you win the lottery is low. More generally, the pr

The probability of winning the lottery if you're a cheater is high, but the probability of being a cheater if you win the lottery is low. More generally, the probability of A conditional on B is not the same as the probability of B conditional on A. Sometimes they're similar, but it depends on the pre-existing odds of A and B.