The probability is 1/3.
While it may seem like it should be 1/2, this is not so. This problem can be restated as follows:
"When two coins are tossed, what is the probability that they both show tails, given that at least one is showing tails?"
When two coins are thrown, there can be four possible equally likely outcomes: T-T T-H H-T and H-H. Now the H-H possibility is discarded, since at least one of the coins is showing tails. Of the other three, only one outcome yields the desired result, and since they are all equally likely, the probability of getting that outcome is 1/3.