I have 2 random variables, A and B, both of which are categorical. I understand that I could calculate their mutual information, which would give me a measure of the information that they share. However, I would like to know how much information is gained about B by knowing that A has a specific value, a. The only name I could think of for something like this would be 'Conditional Mutual Information', i.e. the mutual information of A and B given that A=a.
I am very new to stats, but it seems to me like it would be possible to condition the standard MI formula on A=a, but I don't know if doing that even makes sense. Googling yielded nothing for that name, so I asked here.