You are a Private Detective, you scored the easiest case in the world. All you have to do is sit in
a sleepy town and wait.
On your first day of what you believe is doing nothing and getting paid for it, you get roped into doing a little bit of private detecting for someone, which should only take a few days. Hence the name of the game.
Once word gets around that there is a Private Detective in town, a few people start showing up with their petty small-town problems, none of them can afford to actually pay what a Private Detective normally charges, but one by one you keep getting sucked into it, realizing slowly that all is not what it seems.