I'm wondering where the following *"normalized relative probability distance function"* (for lack of a better name) was first studied:
$$d(A,B) = \mathbb P(\overline A\cup\overline B\mid A\cup B)$$
where $\overline A$ is the complement of $A$.

Googling for "distance between events probability" I found it in Goodman, Mathematics of Data Fusion, 1997, but surely that's not the first occurrence.