Incredible describes something you can't believe because it's so right, like an incredible double rainbow. Incredulous describes how you feel when you can't believe something because it's so wrong, like when someone tells you leprechauns left two pots of gold.
If you pay attention to advertising, we live in an incredible world: Your local team had an incredible comeback. The latest movie is an incredible adventure. Wash your hair with this new shampoo and get incredible shine.
It's enough to make you incredulous, or skeptical.
Incredible isn't just an empty modifier for some new product. The adjective means that what it describes is hard to believe. People use it to mean it's so awesome you can't even believe it. It's usually something good, but bad stuff, like earthquakes, can be hard to believe, too:
He is an incredible player: Hall of Fame talent combined with world-class relentlessness. (New York Times)
Japanese earthquake, tsunami causes incredible damage; effects felt in U.S. (North Jefferson News)
The brain drain out of rural America has been incredible. (Reuters)
Incredulous describes someone unable to believe something, someone being super skeptical. Put your fists on your hips and say "no way!"when you're incredulous. It comes from the Latin incredulous, meaning not believing. Incredulous describes people, and their reactions to things they can't believe:
Asked whether writing the book forced him to seize on moments that he might otherwise have passed over he looked incredulous. (New York Times)
"Do you mean," he began, and paused, scrutinizing her tortured face with disconcerted, incredulous eyes. (F.E. Mills Young)
Something incredible is not credible; it's unbelievable.People, rainbows, and other things can be described as incredible (just check that shampoo label), but only people can feel incredulous, or unbelieving and a little irked.