Question

why can't we find the value for probability of selecting one number in natural numbers by n by n method

Answer 1

You say that each number is chosen with the same probability. Say probability c. Let's denote the probability to choose n by p(n). So you say p(n)=c for any natural n. For any distribution, the sum of probabilities always equals 1:

p(1)+p(2)+p(3)+⋯=1.

So c+c+c+⋯=1. But if c>0, you get

c+c+c+⋯=∞.

And if c=0 you get

c+c+c+⋯=0.

There's no value of c for which this sum equals 1.