Pragmatist is correct, I did not realize that the way I stated the problem was different than the original.

I full understand the solution to this problem.

However, lets look at the original problem. John only knows that one of the man's children is a boy:

1) B, G | 0.33

2) G, B | 0.33

3) G, G | 0.00

4) B, B | 0.33

P(B)|(4) = 1 P(G)| (1,2) = 1

P(B)= .33 P(G) = .66

So lets say that now the woman tells John that the boy is also the eldest:

1) B, G | 0.5

2) G, B | 0.0

3) G, G | 0.0

4) B, B | 0.5

P(B)|(4) = 1 P(G)| (1) = 1
P(B)= .5 P(G) = .5

At first I saw a problem because John obviously knows more given the second piece of information, so the fact that his estimate is worse seemed really weird. What I think is going on here is that his learning more really does decrease his ability to predict the gender of the other child: Before, he had 3 options, 2 of which contained a girl-answer. Now, one of those 2 answers are taken away, so he currently has 2 options, 1 of which contains a girl-answer. As he becomes more informed about the total state of the world, his ability to predict this particular piece of information decreases.