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. Could we say that var(A|B=b) takes the value E[(A-E[A|B])^2| B=b]? Or is it strictly necessary to say it takes the value E[(A-E[A|B=b])^2| B=b]? What is the difference if any