King Conrad was a monarch on an Earth-like planet.
The Second Doctor and Jamie McCrimmon helped him stop his brother Gavin from usurping the throne. Ten years later, the Doctor's and Jamie's past selves (or their doubles) arrived on the planet, having just left an identical planet in which they had helped King Gavin XXIII defeat his brother Conrad. After some initial confusion, the Doctor worked out what was going on and used the TARDIS' fast return switch to bring together King Conrad and King Gavin to learn why the brothers turned out differently.
Gavin and Conrad argued with each other until they tired of it, and the Doctor returned them to their respective planets. (PROSE: Twin Piques)