The chance of finding a secret door directly relates to how many seen tiles are surrounding the door. The more tiles around it are seen, the more likely it is to be found.

Realistically, a player searching near a secret door will almost always have either 5 or 8 of the adjacent tiles seen; so perhaps just check whether the player has seen the two tiles on either side of the door. If the player has seen both, finding the door becomes a lot easier.