Probability is a way of expressing uncertainty. This is the core insight of Bayesian methods. That uncertainty is not an objective universal fact, though. It is specific to your state of knowledge.
If I flip a fair coin and don't look at it as it sits in my hand, the probability of heads is 50%. Your estimate should be the same. Before or after the flip doesn't matter because our state of knowledge is the same.
If I look (and you don't), the probability that it is heads from my state of knowledge is 100% or 0%. Your estimate would be unchanged because you didn't get any more information.
If somebody looks at the coin and tells you what they say, you estimate should be somewhat less than 100% or more than 0% depending on how much you trust them.
All of this is the long way around the barn to say that after the hurricane, the probability that Sandy hit Manhattan is definitely 100%. That's past tense probability, however. It is still also true that the best estimate a year before it hit would be much, much lower. Using words like "probably that a hurricane would hit Manhattan" makes interpretation much harder, of course, because of the uncertain time frame.
It seems to me you're conflating the probability of x happening in the future as assessed from some previous point in time versus the probability of x happening in the past as assessed from the present. Without clarification the wording is ambiguous but I think generally interpreted to mean the former. It would be quite odd to go with the latter as it's rather tautological.
> All of this is the long way around the barn to say that after the hurricane, the probability that Sandy hit Manhattan is definitely 100%
Nobody talks like this in real life. I can't even believe someone bothered to write multiple sentences to try and justify it.
I have never seen this definition used before. I was always taught that probability applies to future events. If I flip a coin the event has happened, me knowing or not knowing the outcome does not change it.
Now you can say after the coin is flipped and you still haven’t looked at the result that the probability of you guessing the correct outcome is 50%.