Not that high, at your library, I'm not sure how they do it, but at my local library, they have you log in with your library card number and a PIN you make. It wouldn't be likely for you to get caught.
If they make you do something like my library does, it would bring you chances of getting caught really high. The police could ask the librarian for logs of people who were on at X time when you bought the laptop and see what websites you went to.