Consider a situation where a person has partial knowledge, but we have a more complete picture. For example, suppose that we want to know the probability that a fish is red. Suppose that the person with partial information knows 1/3 of all fish are red, but we know that the particular species is actually red 2/3 of the time. Do these two separate probabilities have special names? If they don't have any standard names, what would you call them?
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They are called "personal probabilities" in the literature on Bayesian statistics, which is the field where the possibility of different probability assessments among different observers is considered. You could check out the Wikipedia article on Bayesian probability, for instance.
I would call the second of these a conditional probability when trying to emphasise the difference:
The probability of a chosen fish being red is 1/3.
The conditional probability of a fish being red, given that it is species X, is 2/3.