Bertrand's box paradox

There are three boxes, each with two drawers, and each drawer holds one coin. In the first box both coins are gold. In the second both are silver. In the third one is gold and one is silver. The boxes look identical from the outside and so do the drawers.

You pick a box at random, open one of its two drawers at random, and find a gold coin. What is the probability that the other drawer of the same box also holds a gold coin?