What is the name of this statistical interaction? What is the name of the following statistical / informational interaction:

given A, I know exactly what B is.
given B, I know to some extent what A is.

I'm not looking for a probability but rather something like correlation.
Something that tells me that I don't need to include B as a feature when A
is already a feature. A correlation heatmap wouldn't give me this information, but there must be some computation that tells me "Don't include B, it's worthless."

To give some intuition: A could be an item_id and B an item_category.

Or am I wrong? Is it not worthless at all?
You might want to look at conditional entropy, H(A|B) and H(B|A).