This note points out a gap between two natural formulations of
the concept of a proof of knowledge, and shows that in all
natural cases (e.g., NP-statements) this gap can be closed.
The aforementioned formulations differ by whether they refer to
(all possible) probabilistic or deterministic prover strategies.
Unlike in the rest of cryptography, in the current context,
the obvious transformation of probabilistic strategies
to deterministic strategies does not seem to suffice per se.