Question #1. Why do you need to know?
I can say 100 percent evenly. Each private key from 0 to the end of the range has its own public address. Not even own, but most likely shared with another private key.
Question #2. If we are talking about wallets with balances or wallets used once, and about private keys for them. That is another question.
Different programs create private keys on different algorithms. Some just use a random random generator based on ECDSK, others randomly generate their own set of words, from which only then a private key is created using some algorithm. And also on the basis of seeds and sequences. And also there is a creation based on the brain string and its hash.
Plus, their own programs that can create temporary wallets almost sequentially based on the increment of the private key.
On practice. About well-known private keys from used addresses. There is even a graphic table. Most exist at the beginning and end of the range of possible private keys. But these are those that were known at the moment.
But there is another private-public key.
Full range of private keys in hex.
00000000000000000000000000000000000000000000000000000000000000
fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140
But all range public hash160 from public address only.
00000000000000000000000000000000000000
ffffffffffffffffffffffffffffffffffffffff
So in the range of private keys.
000000000000000000000 10000000000000000000000000000000000000000
000000000000000000000 1ffffffffffffffffffffffffffffffffffffffff
We will have, in 50 percent of the private keys, one public hash160 for two private keys. In some percentages, one public hash160 for three private keys. Etc.
This is the number of zeros that we do not take into account first.
And if in the full range of possible private keys? How many repetitions will there be?
In theory.
Given this factor, we can say that private keys are distributed evenly !!!