It depends. We use the term “probability” to cover a variety of different things, which can be handled by similar mathematics but are not the same.
For example, suppose that I’m playing blackjack. Given a certain disposition of cards, I can calculate a probability that asking for the next card will bust me. In this case the state of the world is fixed, and probability measures my ignorance. The fact that I don’t know which card would be dealt to me doesn’t change the fact that there’s a specific card on the top of the deck waiting to be dealt. If I knew more about the situation (perhaps by counting cards) I might have a better idea of which cards could possibly be on top of the deck, but the same card would still be on top of the deck. In this situation, case 1 applies from the choices above.
Alternately consider photons going through a double slit in the classical quantum physics experiment. If the holes are of equal size and geometry, a photon has a 50% chance of passing through each slit (the probabilities can be adjusted, for example by changing the width of one slit). One of the basic results of quantum physics is that the profile of the light through both slits is not the same as the sum of the profiles of the light through each slit. In general, it is not possible to say which slit a given photon when through, and attempting to make that measurement changes the answer. In this situation, case 3 of the above post seems to apply.
My point is that the post’s question can’t be answered for probabilities in general. It depends.
It depends. We use the term “probability” to cover a variety of different things, which can be handled by similar mathematics but are not the same.
For example, suppose that I’m playing blackjack. Given a certain disposition of cards, I can calculate a probability that asking for the next card will bust me. In this case the state of the world is fixed, and probability measures my ignorance. The fact that I don’t know which card would be dealt to me doesn’t change the fact that there’s a specific card on the top of the deck waiting to be dealt. If I knew more about the situation (perhaps by counting cards) I might have a better idea of which cards could possibly be on top of the deck, but the same card would still be on top of the deck. In this situation, case 1 applies from the choices above.
Alternately consider photons going through a double slit in the classical quantum physics experiment. If the holes are of equal size and geometry, a photon has a 50% chance of passing through each slit (the probabilities can be adjusted, for example by changing the width of one slit). One of the basic results of quantum physics is that the profile of the light through both slits is not the same as the sum of the profiles of the light through each slit. In general, it is not possible to say which slit a given photon when through, and attempting to make that measurement changes the answer. In this situation, case 3 of the above post seems to apply.
My point is that the post’s question can’t be answered for probabilities in general. It depends.