Chances are 1/8192
1/8192 is 0.000122070312 and 0.000122070312 is 0.0122%
So, it's a very hard chance of encountering a shiny.
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It depends on luck. when catching a magikarp, you have a 1/8000 chance of shiny.
1/8192. If you're in Diamond, Pearl, or Platinum and have chained a Pokemon species up to 40, however, the chance increases to 1/200, but you have to find a shiny patch in order to successfully get that particular shiny.
The chance of a Pokemon received from an in-game trade being shiny is the same as the chance of capturing a shiny Pokemon in the wild.
Luck. You have a 1 in 8,192 chance of your starter Pokemon to be Shiny.
A shiny Riolu is like any other shiny Pokemon in the game, for every Pokemon that you encounter, there is a 1 in 8192 chance that it will be shiny.