Nice try Kav, but no cigar. In the first place, it's highly debatable whether Poincare was the "greatest mathematical physicist of all time". Most people have never heard of him, and would probably put Newton or Einstein in that place.
This is tricky of you, because in the book Poincare obviously means the question to be a rhetorical one, because he then goes on to explain the laws of probability, law of large numbers, etc. A classic case of quoting out of context.
In any case, it doesn't matter what any so called expert has to say about probability not being certaintly, when you can find out for yourself assuming you have some basic programming skills. Even a spreadsheet analysis will be good enough.
This is another example of taking a scientific term and misinterpreting to mean what it implies in everyday discourse. When you say something is "probable" it means it isn't certain, but in the technical sense "probability" doesn't necessarily mean that. In fact there are several interpretations of what "probability" means, and there is no general consensus, but that doesn't mean you can then triumphantly shout "See! no one even knows what probability IS!".
This is because whatever interpretation you prefer, the math remains the same. The law of large numbers isn't an interpretation but a "law of nature", if you like. Empirical probabilities don't "probably" converge to their theoretical counterparts, they CERTAINLY do.