So, when Abby is able to find him at a cafe, she heads off to confront him alone.
When he says she’s not tough enough to do something like that, she notes that she’s tired of all her hero friends dying while he gets to live.
Of course, it turns out that she didn’t actually poison King at all, but it bought enough time for Gibbs and Torres to find King and arrest him.
Abby gets him to confess by telling him she poisoned his coffee, but is willing to give him the antidote, and he admits to putting the hit out on her when he starts to show signs of the poison.