The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction.
Therefore, your assertion that EVERYTHING has divisibility is a fallacy. You argue above, extensively, that "zero" or "nothing" is an observeable "something" and that, therefore, divisibility does apply to it, yet this cannot be shown in a mathematical equation without contradiction. For example:
To begin with, how do we define division? As you state above, the ratio r of two numbers a and b:
r=a/b
is that number r that satisfies a=r*b.
Well, if b=0, (i.e., we are trying to divide by zero) we have to find a number r such that r*0=a. (1)
But r*0=0
for all numbers r, and so unless a=0 there is no solution of equation (1).
Now you could say that r=infinity satisfies (1).
That's a common way of putting things, but what's infinity? It is not a number! Why not? Because if we treated it like a number we'd run into contradictions. Ask for example what we obtain when adding a number to infinity. The common perception is that infinity plus any number is still infinity.