This is not a question of proof, this is a question of definition. x/y is not defined for y=0.
0/0 is not infinity nor 0. It is not, full stop. At most you can decide by convention that 0/0 should be treated like infinity or 0 in your particular cases.
(though I'm interested if you have pointers about this)
In math, when something is "undefined" it doesn't mean "it is not, full stop." it means that there are multiple answers or no answers with whatever rules we are working with. For example, when you can only work in the field of Real Numbers, the square root of a negative number is undefined (though it is an imaginary number).
In our case, we're saying 0/0 planets (caveat: other than Earth and Mars) have a Linux computer on them; then continuing to say that is 100%. This is clearly not true in any common sense term, since there is not a computer on every planet in the universe. Thus 0/0 == 0% in this case. In real life, the laws of mathematics apply differently than theory. In real life, there is no such thing Zeno's Paradox because eventually you'll reach Planck Scale and then it just depends on how you round, whether you reach the end or not.
0/0 is not infinity nor 0. It is not, full stop. At most you can decide by convention that 0/0 should be treated like infinity or 0 in your particular cases.
(though I'm interested if you have pointers about this)