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I'm not sure if I agree with your definition of belief here (that certain
knowledge is different from and obviates belief). Let me know if my own
(admittedly informal) definition differs from your idea:
To hold a belief X is to act as if X is true.
The reason I like this definition is that it encompasses unconscious
and dispositional beliefs as well as explicit beliefs.
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I would modify the above definition slightly so it would read:
One observed to act as if a statement X were true is said to believe X.
I think is is important to indicate that behavior is the observable. We infer
belief from an individual's acts (one of which may be making the statement "I
believe in X"). Even an individual may observe themself in this fashion.
Reed