Consider the following process of epistemic justification: proposition E-0 is made probable by El, which in turn is made probable by E-2, which is made probable by E-3, and so on. Can this process go on indefinitely? Foundationalists, coherentists, and sceptics claim that it cannot. I argue that it can: there are many infinite regresses of probabilistic reasoning that can be completed. This leads to a new form of epistemic infinitism.