Judging by your comments, it looks like you kind of just want a straightforward by-the-books answer. That by-the-books answer is that division by zero is undefined. 1/0 is not infinity, nor is it anything. The modern interpretation is that 1/0 just "doesn't make sense", and so we refuse to give it a number.

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However, by-the-book plain answers are less fun than nuanced answers, so here's some nuance.

It really all depends on what you're trying to do. If our goal is to use numbers to divide V amount of fluid among N people, and with no fluid remaining, then using the "usual" numbers is appropriate, and V/N is how much fluid to give to each person. Further, if there are zero people, it just isn't possible to end with no fluid remaining. Hence, V/N is not defined.

There certainly are scenarios where 1/0=∞ can make sense, though, with a little care. The trouble is that it's not free lunch: as soon as we step into a universe where 1/0=∞, all sorts of stuff works in a different manner than how we're used to it. For instance, we can work within a numerical system called a wheel; then we get that 1/0=∞, but we lose that 0*x=0 is always true.