Sorry, I didn't mean to imply that probabilities only apply to the future. Probabilities apply only to uncertainty.

That is, given the same set of data, there should be no difference between event A happening, and you having to guess whether or not it happened, and event A not having happened yet—and you having to guess whether or not it will happen.

When you say "apply a probability to something," I think:

"If one were to have to make a decision based on whether or not event A will happen, how would one consider the available data in making this decision?"

The only time event A happening matters is if it happening generated new data. In the Bob-Alice situation, Alice rolling a die in separate room gives zero information to Bob—so whether or not she already rolled it doesn't matter. Here are a couple of different situations to illustrate:

A) Bob and Alice are in different rooms. Alice rolls the die and Bob has to guess the number she rolled. B) Bob has to guess the number that Alice's die will roll. Alice then rolls the die. C) Bob watches alice roll the die, but did not see the outcome. Bob must guess the number rolled. D) Bob is a supercomputer which can factor in every infinitesimal fact about how Alice rolls the die, and the die itself upon seeing the roll. Bob-the-supercomputer watches Alice roll the die, but did not see the outcome.

In situations A, B, and C—whether or not Alice rolls the die before or after Bob's guess is irrelevant. It doesn't change anything about Bob's decison. For all intents and purposes, the questions "What did Alice roll?" and "What will Alice roll?" are exactly the same question. That is: We assume the system is simple enough that rolling a fair die is always the same. In situation D, the questions are different because there's different information available depending on whether or not Alice rolled already. That is, the assumption of a simple-system isn't there because Bob is able to see the complexity of the situation and make the exact same kind of decision. Alice having actually rolled the dice does matter.

I don't quite understand your "likely or not likely" question. To try to answer: If an event is likely to happen, then your uncertainty that it will happen is low. If it is not likely, then your uncertainty that it will happen is high.

(Sorry, I totally did not expect this reply to be so long.)