Essentially what Aurora3500 said. He has a random 1 in 300 chance to spawn in place of another mob in the outer 1/3rd of the map.
Be careful though, if you're playing in Expert, be warned as he's not particularly easy early on in the game due to his new mechanics that were added in 1.3. If you're not too early in the game, it may actually be more efficient to just make a Slime Crown at a Demon Altar, if you have the option to do so.