Incredible means difficult to believe. Incredulous means unwilling or unable to believe. So something that is difficult to believe is incredible, and if you have trouble believing something, you are incredulous.
These adjectives were once variants of each other, but they diverged a few centuries ago, and now they are no longer considered interchangeable. They are still occasionally mixed up, but many readers will consider this an error.
What we’re seeing is quite incredible because this is the oldest society in the Arab world. [CNN]
Wentworth was incredulous when Bancroft revealed, accurately, that France was willing to ally with America without the promise of much in return. [Edward Bancroft: Scientist, Author, Spy, Thomas J. Schaeper]
David Nabity, one of the leading proponents of the recall, was incredulous that the measure had apparently failed. [New York Times]
It was an incredible story, a fabulous story; the sort of head-shaking, who’d-a-thunk anecdote suited to an entry in Ripley’s Believe It or Not. [Moby-Duck, Donovan Hohn]
[T]heir campaigns are probably over, for all intents, barring an incredible comeback. [Los Angeles Times]
Neighbors were incredulous Bilotto would have a firearm with four kids, let alone an illegal one. [Gothamist]