Male bears, first solution to the last question

Since it's now given that the lighter bear is male there are only two possible outcomes (mf, mm). Thus the probability that both are male goes up to 1/2. Note how each additional piece of information changed the number of possibilities and, hence, the probability of the outcome.

Male bears, second solution to the last question

The sequence of three question is supposed to lead one on to wondering what difference does it make to specify that the white bear is male. And, in my experience, the trick works too. But since it's now known that the white bear is male, its sex is removed from the realm of random. All that matters is the sex of the dark bear who is believed to be male with the probability of 1/2. A short way to express the same idea is as follows:

where P(A|B) means the (conditional) probability of A provided B is known to take place.

Reference