Suppose I flip two coins, without letting you see the outcome, and I tell you that at least one of the coins came up heads, what is the probability that the other coin is also heads?
Hint: The answer isn't 1/2.
You might initially think that the answer is 1/2, however, it isn't.
Before I tell you anything, all you know is I've flipped two coins, and the possible outcomes are:
HH, HT, TH, TT
I now tell you that there was at least one head, which eliminates TT, leaving three possibilities. Of these three possibilities, only 1 allows the second head: HH. So the probability is 1/3. QED.