That is the chances of encountering a shiny Pokemon. My first encounter with one was an Exeggcute, in the Safari Zone(FR). I was not successful at capturing.
Fast forward two years to me going through a new play of LG. I just made it to Six Island, and surfed next to the braille door. Then, a wild encounter.
I wasn't surprised, as I had seen three on my way down. But after its battle cry, I didn't immediately release my Pokemon. I heard a sparkle sound, and noticed that this Marill was colored closer to teal than dark blue.
My eyes widened as I realized what was happening, and quickly I swapped out my lvl 52 Lapras for a 15 Onix. I chose strength for my attack, and winced as I saw the Shiny's hp dwindle. When it stopped just above half health, I released the breath I was holding in, and prayed that what I did next would work.
Ultra Ball, go!