Check out the show "First 48" on A&E, documentary-type show about homicide detectives working cases.
About 90% of the time they bring in a suspect, they have no hard evidence against them. The police work the old good cop/bad cop standby, and amazingly it still works. Instead of lawyering up, the suspects operate their mouths until they are in deep trouble. If they are smart enough to say nothing, or just lawyer up, the police stay at square zero.
A lot of these people on the show are guilty and usually break down and give full confessions, but sometimes they bring in someone who was merely present at a homicide, and they too operate their mouths unncessarily until police have evidence to "put them at the scene" at which point the "felony murder charge" is brought against them (which means that a person can be charged with a murder that they didn't actually commit.)
I'm not trying to advocate advice on how to get away with murder, but police can be like prosecuting attorneys, casting a wide net in order to get as many arrests and press as many charges as possible, and aren't particularly worried about whether or not their arrestees deserve to be prosecuted, just so long as they can be prosecuted.