"The Pokérus had a 3 in 65,536 chance to be on a generated Pokémon, either wild or bred. Through battling or capturing this wild Pokémon, players could get this helpful virus onto their own Pokémon, and subsequently spread it around. Due to the overwhelmingly low chance of encountering the virus (about 1/3 of the chance to encounter a Shiny Pokémon), and the fact that most would not even recognize a Pokémon with the virus and therefore flee from it, many players would never have a Pokémon with the virus."
This is written by Bulbapedia, not me.
