Why, nonsense, the probability 3 event and the regular event could be the sort of things that never happen at the same time, in which case the probability of their intersection is 0.  Say, the chance that Keltham is wearing holding a silver coin is 0.5, and the chance that Keltham is not holding a silver coin is 3.  The chance that Keltham is holding and not holding a silver coin is surely 0.

Why, nonsense, the probability 3 event and the regular event could be the sort of things that never happen at the same time, in which case the probability of their intersection is 0.  Say, the chance that Keltham is holding a silver coin is 0.5, and the chance that Keltham is not holding a silver coin is 3.  The chance that Keltham is holding and not holding a silver coin is surely 0.