I immagine that in Universe 3, Goku never arrived on Earth... so Piccolo had no problems in becoming king of the planet. After three years of training, he finally surpassed Kami and went to the Palace to finally challenge him... Kami was not powerful enough to keep his evil half from winning
(let me remind you, that if Piccolo hadn't trained, Kami would have beaten him with one finger...)
After defeating him, Piccolo forced Kami to fuse with him, or Popo would die...

my version of King Vegeta's death in universe 3...