To see this, let us call one of the dogs X and the other Y. Initially we have four equally likely possibilities:
X=Male, Y=Male
X=Male, Y=Female
X=Female, Y=Male
X=Female, Y=Female
This is our starting point. If the question were simply, “What is the probability that two randomly chosen dogs are both males?” then the correct answer would be 1/4. (This would be a good time to state explicitly that we assume that males and females are equally likely.)
However, we receive information from the fellow giving them a bath that allows us to update our probabilities. We learn that one of the dogs is a male. That means that option four now has a probability of zero. But this information does nothing to affect our assessments that the first three possibilities are equally likely. That is, the revelation that one of the dogs is a male is true regardless of which of the three scenarios we are in.
So we have three, equally likely possibilities, and in only one of them are both dogs male. So the answer is 1/3.