For a finite set $N = \{1,2,3, \ldots, n\}$, a permutation over $N$ is a bijective function $\pi: N \to N$. A uniform distribution over the set of all permutations of $N$ must assign each permutation $\pi$ with the same probability $\frac{1}{n!}$.
For a countably infinite set, say, the set of all natural numbers, $\mathbb{N}$, a permutation is also a bijective function $\pi: \mathbb{N} \to \mathbb{N}$. Does there exist a uniform distribution on the set of all permutations of $\mathbb{N}$?