Random Positive Integer [Request]

I‘m in a debate. here is the premise:

let’s say that you select any random positive integer and look at it. then you take any other unique random positive integer.

What are the odds that the second integer will be greater than the first integer?

My argument is that there is a 99.99999999…% chance that the second number will be greater than the first, because we are talking about an infinite set of numbers greater than the first, and a finite set of numbers less than the first.

My entire group chat’s stance is that it is 50/50, or there is no way to really tell.

What is the best answer?