What is the difference in usage between ability and capability?
Capability implies unrealised potential, as in "John is capable of winning", which implies John has the ability to win but it's not definite. It means more or less "John has the talent that's needed to win."
Ability, on the other hand, implies possibility. "John is able to win" means John is in the running to win but not necessarily that he has the skills or ability to win. It means more or less "It's possible that John will win".
But here's where it gets more confusing:
"John is able to read" means John can read without doubt, whereas "John is capable of reading" means John has all the necessary brain power and whatnot to be able to read but the question of whether or not he can read at the moment is left unsaid (although the fact that someone does say "John is capable of reading" probably means John can't read right now).
There's another shade of meaning not yet touched upon. able can also be of things, "of a thing (esp. a boat): strong, substantial, well built; or a person who is intelligent, skillful, apt, talented, or clever (OED). Compare, "It is an able ship/It is a capable ship." They are both meaningful, but I would be more likely to use the first one. Another example, "She is an able tour guide/she is a capable tour guide". The second sounds contrived to me, even a little damning.
It's also interesting to note that they entered English through different sources, and that able is the older of the two.
I want to give only one condense sentence, so that you can easily to remember.
Capability often refers to extremes of ability.
I have the ability to write, but I don’t have the capability to write a novel.
Ability vs. capability vs. capacity on Grammarist