Ethics class

I told you guys in one of my posts that I am in police foundations.. ye so in police foundations everyone has to take an ethics course... My teacher told me that the stuff we are learning is on par with a second year uoft ethics class. because he went to uoft and he just took his second year ethics class and is teaching it to us. We are 1st year college students, so some of the stuff goes right over my head sometimes lol. I'm not gonna lie to you.. but some of that stuff is incredibly interesting.. He basically gives us certain ethics theories and gives us the example...really interesting stuff. I'm just going to say a example.. actually its sorta one of our assignments.

Basically your in a dilemma.. and that dilemma is you are a police officer in a small town, you are the chief inspector, I guess you can call it. You get a call and basically, you hear that a 5 year old little girl has been raped and murdered... now here's the problem, you have no leads. No suspects, NO NOTHING.... The case eventually goes national, so obviously everyone in this little town knows about it. Now everyone in the town suspects one person.. that person is basically the town crazy, the town idiot. So you eventually bring this guy into custody.. you question him.. its gets to the point where the guy tells you he has a solid alibi. time and place.. could have not committed the crime.. while having the guy in custody.. everyone in the town is waiting outside. They are basically outside waiting for him to come out to kill him. They will not listen to reason because this crowd no matter what they hear. They believe 100% that this man committed the crime. So they are going to kill this man..

You have two options:
1) You let this man go outside and he gets killed by the crowd, you lose your job.
2) You send this man to jail.. making everyone happy..But he is Innocent.. so your sending a Innocent man to jail, he will probably be raped and killed in jail. because rape is the most vile and disgusting thing you can do according to prisoners.. killing a police officer is the best thing... you will be treated with respect.. fyi

This is suppose to be unsolvable.. since it is unsolvable we basically pick one of the theories our teacher taught us to try and explain why we picked either 1 or 2..... either way this Innocent man is going to have something bad happen to him. WHAT WOULD YOU DO?