What is the chance of getting a shiny AND a hidden ability Pokemon in Kiloude City Friend Safari or horde battles?
In Generation 6, the chance of encountering a Shiny Pokémon is 1:4096. In horde battles, this works out to be a chance of
5:4096 (ca. 1:819) 1:819.6. 1-((x-1)/x)^5
The chance to find a Pokémon with a hidden ability is not fixed (I don't have any information about it, because I didn't play Gen V/VI much and don't know the chance to get the hidden abilities).
The best idea is to catch a male pokemon with the hidden ability and take it in the pension with a ditto. The chance that the hidden ability gets inherited is 60%. So the chance is 1:6827.