Sure.
And you as the player are the one who decides what the metaphorical wind is like for your character's attitude towards the people and world around them.
Don't trust the king? Good news, you can tell the DM that, and they can't say "yes you do" unless you are affected by magic. They also can't roll the king's Persuasion to change your character's mind about that without you agreeing to how the DC is set, including potentially a straight contested roll.
Or, to put it another way:
Just because they didn't find a trap in the hallway doesn't mean they have to think there isn't one, especially if there's a posted sign saying "This hallway is trapped."