Question: Say we have two random variables A and B. Is it correct to say that if B takes value b, then the random variable var(A|B),

Say we have two random variables A and B. Is it correct to say that if B takes value b, then the random variable var(A|B), which is originally not the same as the numerical value var(A|B=b), actually takes a specific value, because we now know little b. Why is it wrong that var(A|B=b) takes the value E[(A-E[A])^2| B=b]? Is it because here we don't convey the available information about B to the variance that is calculated

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