In this paper, I introduce a new principle in the logic of conditionals. Suppose there has been a murder on the estate. I claim that (1) implies (2):
(1) If the driver hadn't done it, then either the butler or the gardener would have.
(2) If the driver hadn't done it, then if the butler hadn't done it, the gardener would have.
I develop a series of arguments that this inference is valid. Then I show that several commonly accepted principles about conditionals (for example, Modus Ponens) lead to paradoxical results when combined with this one. To validate the principle, and explain why Modus Ponens fails, I offer a new theory of conditionals, involving a distinctive method of revising a body of information with an antecedent.