Gen V:
Okay, first Hidden Ability.
In Generation V, female Pokémon with Hidden Abilities have a 60% chance of passing on the Hidden Ability to their offspring when bred with a male Pokémon from the same Egg Group. For example, if a female Darmanitan with Zen Mode breeds with a male Simisage, the offspring Darumaka may have Inner Focus instead of the usual Hustle, and would evolve into a Darmanitan with Zen Mode (instead of Sheer Force). Hidden Abilities cannot be passed down from male or genderless Pokémon, and will not be passed down if the female was paired with a Ditto. Source.
This means there is a 3/5 chance the baby will have the Hidden Ability.
In Generation V, the Masuda method's success rate increased from 5/8192 (~1/1639) to 6/8192 (~1/1366). (Source: Same as above)
So, there is a 6/8192 chance the baby will be shiny using Masuda Method.
Now, doing an overly complicated mathematical procedure called multiplication, we get:
3/5 x 6/8192 = 18/40960
18/40960 = 1/2275.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555
= ~1/2275, or about 0.044%
.: The chance of this happening is 1/2275.
Gen VI:
Okay, first Hidden Ability.
Hidden ability chance is the same as before, or 3/5.
Since shiny chance is halved, this means Masuda Method's chance is also halved. Therefore, half of 6/8192 is 6/4096. Source.
Again, doing the post-collage level of calculus called multiplication, we get:
3/5 x 6/4096 = 18/20480
18/20480 = 1/1137.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
= ~1/1137, or about 0.088%
.: The chance of this happening is 1/1137.
