How many characters you need to mistype at minimum to get another valid address? Is it known the minimum amount of characters you need to mistype to get another valid address?

Addresses contain checksums, and also must follow some specific rules, so I guess this could be calculated: I wonder if someone did.
Check sum is a result of 2 hash-functions: SHA256 and RIPEMD160. The length of checksum is 4 bytes. Hash functions are indistinguishable from random oracle, so it is possible, if you make 1 mistake in non-checksum character, you get the same checksum. But probability of this is 1/2^32.

Added later: not exactly correct due to base58 encoding. Correction in the another answer.