Agreed, probabilities are conditional on an information set, and an information set can be related to the passage of time, but it can be related to other things also. In a relativistic universe, the set of things that have "already happened" is not even uniquely defined
We could imagine a group of people sitting around a table, playing a card game. Each one sees his own hand, but not the hands of the others. The different players have different probabilities of different outcomes, because they have different information - time playing no role here. Similarly, it makes perfect sense, after the hand is played and everyone sees all the cards, to discuss what the correct strategy for a particular player was,
given the information available to that player when he had to formulate the strategy, even though we now know exactly which cards each player has. Does it make sense to say, the player to my left had the ace of hearts, therefore the correct strategy would have been (whatever)? Everyone knows now the player to my left had the ace of hearts, but at the time I had to decide which card to play, I didn't know that. It makes perfect sense to talk about the probabilities that different players had the ace of hearts, even though after the fact, we know who it was.
The important thing for probabilities is what you know, not what time it is. The two can be related, but they're not the same. As your example points out.
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