There are three alternatives I can think of:

1) The universe has a joint probability distribution such that events are not independent, but so few events are independent that limiting the description to a causal one does not materially reduce the complexity of the "true" model. In this case, There would only be the joint look-up table.

2) All events are independent.

3) The universe is not well-described by the laws of probability.

The first case would make prediction pretty much impossible (since you're never dealing with the exact same set of variables twice). "Same river" and all that. No prediction more specific than "the universe persists in some way" would be true very often on average, since there are so many possible outcomes, and no reason to believe that the next joint probability for the event you care about is similar to the last one.

In the second, you could predict roughly the proportion of events based on the proportion of past events, but there would be no discernible pattern, or result of action.

In the third, I can't tell you what you're likely to observe, for obvious reasons.