I've discussed characters here before and one of the points I've made was about the writer's need to understand that the people with whom they populate their stories don't know they're in books/movies/plays/television commercials. They think they're living their lives and some incident just happens... to them.
That's the thing. Each character you write believes the story is his and his alone (I'm saying "his" rather than "his or hers" to speed things up and not to make a point about gender. Feel free to read "hers" and I promise you I'll be making the same point.). Each one of them is going to go home tonight and tell the wife/husband/child/uninterested bystander, "Guess what happened to me today."
So let's consider the plight of Cop #3.
In a screenplay, Cop #3 is the one brought in probably just to slap on the handcuffs and begin (they never get all the way through) to read the suspect (let's face it, guilty party) his rights. From a story function, that is all Cop #3 is going to do. He'll never appear in the story again and doesn't even merit having a name.
The same can certainly be true in a crime novel. Cop #3 isn't identified that way, but serves the same purpose: He cuffs the villain and leads him out of the room, just so the reader knows the killer has been properly arrested and removed from the premises. It is incredibly easy to think of Cop #3 as a plot function and forget him.
But you shouldn't. There is always some bit of emotion or color you can get out of Cop #3 if you try hard enough. Because in a film, TV show, stage play or Christmas pageant (and the seasonal music is already starting, just to drive some of us mad), that role will be played by an actor who is almost certainly going to be a human. That person has spent years working on his craft and this is as far as he's gotten so far. He's going to be thinking about how to read those Miranda rights all night before shooting and how to be noticed in a part that was written by someone who thought of him as Cop #3.
So if you consider the character that way--as a person--you might consider what reaction Cop #3 will have to entering the room. Will he be earnest and serious? Amused by the situation? Revulsed by what he's found in the space he's entered? Annoyed that his donut break has been interrupted? All of these, and a thousand more, are completely legitimate possibilities. Any one of them will give your scene more humanity than simply sending in a stick figure with a pair of handcuffs.
I'm not suggesting that a novelist needs to write into the chapter Cop #3's complete backstory, his unhappy childhood and desire to serve the community to spare others the awful experiences he had to endure. You don't even need to know what Cop #3 had for breakfast before walking in unless he's going to be so nauseated we'll all get to see it, which I don't recommend.
What you should be able to decide is the attitude Cop #3 brings to the situation, whatever that might be. That will lend him some reality and some possibilities to make your scene more interesting. And that's always a good proposition.
So get to know Cop #3. Just a little bit. It'll make your writing better.