When encountering a wild Pokémon, you have a 1/8192 chance to encounter a shiny Pokémon in the wild. With the odds essentially being a 0.012% chance I would go months without finding a shiny, but I was once lucky enough to find two in a short period of time.
I have played a majority of the Pokémon Games, starting with Red/Blue/Yellow up until Alpha Sapphire being the latest I have played, but there is one thing I have never encountered before: An NPC with a shiny Pokémon.
Is it possible for an NPC Trainer, such as a Gym Leader or the Elite 4, to have a shiny Pokémon? If so, would the odds still be 1/8192 or are the odds different?