The Shores of the Dirac Sea has a somewhat head-scratching puzzle about probabilities:

Let us say that someone gives you a lopsided bet. Say that with probability \(r\) one gets heads, and with probability \(1-r\) one gets tails, and you have to pick heads or tails. You only know the outcome of the first event. Let's say after the first toss it came out heads. What is the probability that \(r > \frac{1}{2}\)?