Divination is something connected directly to the idea of stepping outside the boudaries of the normal social order. In particular in Greece this is the case, where diviners are associated with the outskirts of society, not with its mainstream.
In fact, divination could, potentially, be tied directly to sex. Plato tells us that Eros is the intermediary between the gods and men, and that divination belongs entirely to him.
Curiously, Plato also includes "the art of the priests concerning sacrifice and initiations, just like the incantations, prophecy in general, and magic goeteia."
I think that, really, we need to re-visit the connection of divination and sex, and seriously think about how the two events are similar, if in state of mind or in myth.