The first example isn't very good. I see what they're trying to do there, to collapse the ambiguity about which child is the boy. But if you work from the set of possible scenarios just purely from those that match the description, without assuming any methods or probability distributions on the way Mr Smith selected the child to go walking with, you get 1/3.

I advise students to always work this through from the combinations of possible scenarios.

The deeper truth of the vos Savant story is that verbal descriptions are ambiguous, and the even deeper truth is that probability calculations are highly volatile on information.

Eventually disagreements come down (among people who can competently do the calculations) to arguments about what such and such a phrase means, or what underlying probability distribution it implies.

Hence in the Monte Hall Problem, there is no advantage to switching if Monte selects the unchosen door to open at random, and it happens to be a goat. That situation is consistent with the description, but perhaps not the 'feel' of the game show setup.

In science, it is wise to be aware of this. If you have probability calculations that are so volatile based on interpretation, then you probably want to avoid trusting the results, no matter how careful your hermeneutic.