Easy conditional probability question

Tia and Jerry are tossing two coins. Tia wins when both coins turn up tails. The coins are tossed but roll under a chair. Jerry looks under the chair and, seeing both coins, says, "At least one of them is tails." What is the probability that Tia wins?

The way I thought of it was:

P(Both tails | At least one tail)

= \frac{P(both tails)}{P(at least one tails)}

= \frac{\frac{1}{2}}{\frac{1}{4}}

But the answer in the book is \frac{1}{3}

Can anyone tell me where I'm going wrong/how I should be doing questions like this? Thanks!