Chance that first 6 characters of a SHA-1 hash matching another SHA-1 hash? Just what the question says -- what is the chance that the first six characters of a SHA-1 hash will match the first six characters of any given SHA-1 hash?

A SHA-1 hash is supposed to be almost random, so I'd say
$$P = \frac{1}{256^6} \approx 3.55 \cdot 10^{-15}$$
Assuming you mean "byte" by character. However, this might only be approximate, as the algorithm is quite complex. If you mean HEX-Digit representation, it would be a base of $16$ i.E.
$$P = \frac{1}{16^6} \approx 5.96 \cdot 10^{-8}$$
