Starting in Black 2 and White 2, this mechanic was updated so that females had an 80% chance of passing down their Ability slot, period. In Black 2 and White 2, this same 80% chance does not apply if a female Pokémon is bred with a Ditto, but starting in Pokémon X and Y, it does.

So 80% chance of passing down ability if female parent, no matter what. Even if it's a hidden ability, I believe it's still an 80% chance of passing it down to the child.

Before Generation VI, it was not possible for male or genderless Pokémon to pass down their Ability in any way. Starting in Generation VI, however, if these Pokémon have their Hidden Ability and are bred with Ditto, they have a 20% chance to pass it down to their offspring. Ditto's Ability is always irrelevant to inheritance.

This statement applies to males only. So 20% chance to pass down hidden abilities. Otherwise if it doesn't have a hidden ability and you were to breed the male with a ditto, then it's just 50% for a certain ability, assuming there's two.