CRC64(s) is a 64-bit value, where s is a string of an arbitrary length. The change of one character causes the value of CRC64 to change. All values are used. Does this mean that the probabity of
$$CRC64(s_1) = CRC64(s_2) = \frac{1}{2^{64}},$$
given $s_1$ and $s_2$ are arbitrary strings (length and contents are unknown)?
(I think this is the case but maybe we need to apply more properties of CRC...)