There is no general answer—this question goes to why do you consider a particular data point to be evidence suitable for updating your prior. Ideally you have causal (structural) knowledge about the relationship between A & B, but lacking that you probably should have some model (implicit or explicit) about that relationship. The relationship does not have to be linear and does not have to show up as correlation (though it, of course, might).
There is no general answer—this question goes to why do you consider a particular data point to be evidence suitable for updating your prior. Ideally you have causal (structural) knowledge about the relationship between A & B, but lacking that you probably should have some model (implicit or explicit) about that relationship. The relationship does not have to be linear and does not have to show up as correlation (though it, of course, might).