The chances for the options are either unchanging or based on your reputation with the tagged city, which is usually the major city closest to that region (or Wimborn if that region is not tagged with a city). The chance that a freed captive offers you a reward is also based on reputation. It has zero chance at -5 rep and always happens at 15 rep.
Asking for no reward always gives +1 rep. (+1 to 2 rep for releasing them)
Asking for a material reward has a 75% chance of gold, and a 25% chance of an item. The item has a 75% chance of being enchanted, and the type of item depends on the level range of the region.
Asking for sex has a 10% chance to succeed at -50 rep and a 60% chance at 50 rep.
Asking them to join you has a 7.5% chance to succeed at -50 rep and a 32.5% chance at 50 rep.