[Question] Probabilities sensitive to the form of the question?

I've been reading Machine Learning - A Probabilistic Perspective by Kevin P. Murphy. Each chapter features exercises and one that seems incredibly simple has me completely baffled.

Here's the exercise:

Probabilities are sensitive to the form of the question that was used to generate the answer.

(Source: Minka.) My neighbor has two children. Assuming the gender of a child is like a coin flip, it is most likely, a priori, that my neighbor has one boy and one girl, with probability 1/2. The other possibilities—two boys or two girls—have probabilities 1/4 and 1/4.

a. Suppose I ask him whether he has any boys and he says yes. What is the possibility that one child is a girl?

b. Suppose instead that I happen to see one of his children run by, and it is a boy. What is the porbability that the other child is a girl?

As I understand it a. and b. are identical. But they wouldn't be asking the question if that was the case.

What am I missing?