A jury trial of your peers is a rare thing these days. This is how it would go down:
The investigator says "who's been downloading CP?" and everyone looks at you. Probably because you're the weirdo internet geek among the family/roommates. They now have a suspect, and nothing you say then will convince them otherwise. They interview everyone separately leading the conversation to get statements about circumstantial things that out of context don't make you look good.
It's enough to get a search & data warrant. They take your phone, your PC, all your hard drives, and pull every website you've ever accessed and every email you've ever received or sent. They trawl through this for anything out of place, or which can be construed out of context to be something they can pin on you. This is no longer about CP--they "know" you are guilty, but the fact that they can't find any CP on your computer just means your smart enough to know how to hide it. Now they're just trying to find something to stick to put you away. The Al Capone nail-him-on-tax-evasion-or-whatever-sticks strategy.
You don't hear anything for a while so you think this whole thing is behind you, and you're just pissed you can't get your PC and phone back. Then they show up and arrest you. Your lawyer explains there are five felony charges against you, including the CP thing, and you're looking at 30 years to life where the survival time of a CP convict in the general population is about 3 days. The evidence is flimsy and you can fight these charges in court, but it'll cost you hundreds of thousands of dollars in legal fees and your success at winning all counts is really up to the whims of the judge and/or jury. The DA offers a plea deal: 3 years house arrest, community service, and registration on the sex offenders list, but critically: no prison. The weekend is coming and you're going to be shipped out from the local police lockbox to county jail. The DA is dragging his feet on getting you into protective custody. You sign the plea deal and walk out alive, but fucked for life.
Welcome to the modern criminal justice system.
[This more or less happened to a college roommate of mine (not CP though), and a Tor developer I knew through work.]