How likely is a latent to produce a false positive? What if the police burst into your house and start dusting for prints because they're "collecting evidence."

How likely is a latent to produce a false positive? What if the police burst into your house and start dusting for prints because they're "collecting evidence." They then run those prints through their database of existing prints, match you to a crime in another state for which you have an alibi, and arrest you. You're held without bail because it was a violent crime, and your presence in another state at the time of arrest marks you as a flight risk. Because the court where your trial will be held has a several month backlog, you spend several months in jail. On the first day of the trial, evidence is heard of your alibi, which exonerates you. How would that be just for any of the parties involved?