I have two teenagers. One is a boy of 13.

Do we encounter a similar situation with regard to the odds of the second teenager being a boy?

edit: I'm thinking the odds are exactly the same, 13/27, by coincidence, as there are seven possible teen ages.

So then, what about this: One is a boy named George. Or One wears a black shirt. Or One likes chocolate.

Doesn't this mean that the more information we gain about the boy, the less likely it makes it that his sibling is a brother?

More likely, but only if that information being true was a precondition for knowing about the boy in the first place. Take the following scenarios, assuming Alice knows Bob has exactly two children.

Alice: Do you have a son? Bob: Yes Alice: Pick one of your sons, and tell me the day of the week he was born Bob: Sunday

Here the day of week provides no additional information because Bob will always have an answer (like in Monty Hall, where Monty will always reveal a losing door), so the probability that Bob has two boys is 1/3.

Alice: Do you have a son who was born on a Sunday? Bob: Yes

Here having a son isn't enough; he also has to satisfy a condition that occurs with only 1/7 probability. Bob is more likely to be able to answer yes if he has two sons and thus two chances to satisfy that condition.