Inquisitors are more effective at preaching when in an enemy dominion. Their priest level counts as double for the purposes of preaching. Their chance of increasing dominion through preaching is thus (60% times the priest level) minus (5% times the enemy dominion level).
Example: a Marignon inquisitor of level 2 would have a 100% chance of increasing dominion in a province with -4 dominion. In a neutral or friendly dominion province, his chance for success would be the same as any other level 2 priest: 60%.