This is the crux of the "paradox," which is really just an interpretation problem. Most people assume that the question asks exactly your scenario, i.e. if a specific child is selected and it's a girl, what's the probability that the sibling is also a girl? In that case, the event space is just GB or GG, and p(GG)/(p(GB) + p(GG)) = 0.5. (BG is not in the event space because we are conditioning on a specific child being a girl.)

However, if the question is interpreted as "what's the probability of having two girls if we know there aren't two boys," then the event space is GB, BG, GG, and p(GG)/(p(GB) + p(BG) + p(GG)) = 1/3. Both GB and BG are in the event space because we are not conditioning on the sex of one specific child.