[Unarmed]

I would have potted the flop, mostly because a < half pot bet multiway generally means Villain has whiffed. (from my experience, we've had this discussion before) Given you called multiway you're announcing that you don't have a hand. (as did UTG) BB either has a monster or has recognized this and is betting with nothing. Unfortunately, you have no hand so you really have no business trying to figure out which one it is.