Is there uniform probability of natural number?

Question

I know that https://en.wikipedia.org/wiki/Natural_density

But, I want to know if there is uniform probability in every subset of natural numbers.

It means,

1. every subset $A \subset \mathbb{N}$, $P(A)$ is well-defined, $0 \leq P(A) \leq 1$

2. $P( \emptyset )=0$, $P(\mathbb{N})=1$

3. $A=\sqcup A_i$ (disjoint union), $P(A) = P(A_1 )+...+P(A_n )$

4. $P(A+n)=P(A)$ (Here, $A+n = \{ a+n \in \mathbb{N} ~|~ a \in A\}$ )

Or is there a counter example that shows that such a uniform probability distribution does not exist?