The answer most people jump to is 1/2, since we've had it drilled into us that coins are independent, so the outcome of one shouldn't affect the other. But the phrasing of the question contains a subtle trick. By stating that one of the coins is showing heads, I have eliminated the possibility that both coins are showing tails. But there are actually three remaining possibilities: heads/tails, tails/heads, or heads/heads. In only one of these three are both coins heads, so the answer is in fact 1/3.
The trickiness of the phrasing comes from the fact that when we say that one of the coins is heads, we deliberately don't say which one. We could say equivalently that at least one is showing heads. The probability is the expected 1/2 once we specify ahead of time which coin it is.
Given this preliminary, consider the following problem, which has been making its way around the Web of late:
I have two children, one of whom is a boy born on a Tuesday. What is the probability the other one is a boy? (You can make all the expected simplifying assumptions: no twins, boys and girls born in equal proportions, each day of the week is equally likely, etc. It's a math problem, not an obstetrics exercise.)
I will post the answer in a few days.