Cats might pee on something if they have a urinary tract infection or some other medical problem. They might pee on things if their litter boxes aren't clean enough (or there aren't enough boxes... one per cat plus one extra is usually considered best depending on the size/stories of the house) They might pee on something if they are angry about things (new pet, moving, baby)
The best thing to do to keep cats from peeing on things depends on why they are peeing. Medical and obviously you have a vet solve it, an upset in the home and you have to work on helping them adjust possibly by breaking the house up into zones, litter boxes and you clean more and/or get more (definitely make sure there is at least one litter box on each story of your home if not just doing 1/cat+1) especially for the basement in case they get locked down.
as for washing the smell out, unless you wash with an animal ezyme wash, the smell will always exist for the cat and the cat will continue to pee on it if they can reach. Otherwise I've always found washing with a lot of vinegar does the trick. Our cat reacted VERY badly to a new dog in the home and started peeing on all my husbands clothes and our bathroom rugs so I have a bit of experience there hehe. all the other suggestions sound good too such as bac out or borax

but yes, even though you won't smell it, the cat probably will so be wary.