To be clear:
1) nobles in enemy territory (at War with the region's owner) who have no unit or only wounded soldiers can be captured automatically at turn change by the game, no player involvement required. The "only wounded soldiers" part is a bit unclear. I've had it happen to me when I only had a couple men, all wounded. So far as I know, doing police work or having police forces in the region has no effect at all on the chance to be captured. Infiltrators have a reduced chance of being arrested this way.
2) priests are *not* subject to automatic capture at turn change, nor are adventurers.
2a) adventurers can be arrested by any noble with a unit. (Have to be in your own realm, maybe?)
2b) priests can be arrested by a noble with a police unit only if they are members of the same realm as the arresting noble, or are at war with the arresting noble. In addition, they must be in a region owned by the arresting noble's realm, or in a regon under a TO.
3) infiltrators can be arrested any time they do an illegal action. They will be put in the prison of the realm against which they comitted a crime. Using the police option of "Patrol the streets" will increase the chances of the infil getting caught.