Since I see no value in secretly determining whether the character succeed at something without rolling dice, passive checks can only represent the average result for a task done repeatedly in my games. (Those are the two things that passive checks are for, according to the rules.)
As such, a player may establish repeatedly searching for secret doors while traveling in an environment that may contain secret doors. This will be an uncommon situation, chiefly associated with a more abstracted travel scenario where, for example, finding secret routes through the area cuts down on travel time. The player is likely trading that off against staying alert to danger which means that he or she has no chance of avoiding surprise or noticing traps in the front rank of the marching order, unless the character is a ranger in favored terrain.
Generally speaking, a character is going to find a secret door in my game by way of the player engaging with the environment in which I have telegraphed the presence of a secret door. Depending on the player's goal and approach, he or she may make an ability check to find it, probably Wisdom (Perception). Once found, the secret door then requires some effort to figure out how it operates which - again, depending on the player's stated goal and approach - may call for an Intelligence (Investigation) check.