The answer in analysis is to identify the result of all the “infinitely many integer divisions” with the end point.
Yes, you’re right, at any finite subdivision along the way from point a, you haven’t yet reached point b. However, once you say you’ve genuinely stepped through the infinitely many sub distances, then you have found yourself at point b. This is what we mean when we talk about the limit of a converging series with a variable tending towards infinity being well defined.
This is possible in reality, as Aristotle understood, because Time is also a relevant dimension in motion and you pass each of your gradually shrinking distances in gradually less time. The time dimension can also be factored into analysis and it’s limits defined and understood in the same way.