This example along with all the similar ones drives home the basic idea that probability is tied to its model and its model is often best phrased as a generativ

This example along with all the similar ones drives home the basic idea that probability is tied to its model and its model is often best phrased as a generative story. If we agree on the generative story we'll agree on the model and then your intuition probably works just fine. In situations where the story is obscured—in this case, only the end results are mentioned so that the story is ambiguous—then you can have ambiguous answers.