This conditional probability problem makes no sense to me intuitively

"The king comes from a family of 2 children. What is the probability that the other child is his sister?"

I know if I work through this problem using conditional probability concepts, the answer is 2/3.

However, could someone explain why this is the answer?

I don't see why this question is any different from the following:

"A coin is flipped 2 times. The first flip lands on heads. What is the probability that the second flip lands on tails?"

Yet the answer to the second question seems to obviously be 1/2.