SHAMBLING sleuth Columbo always gets his man. Take the society photographer in a 1974 episode of the cult US television series who has killed his wife and disguised it as a bungled kidnapping. It is the perfect crime – until the hangdog detective hits on a cunning ruse to expose it. He induces the murderer to grab from a shelf of 12 cameras the exact one used to snap the victim before she was killed. “You just incriminated yourself, sir,” says a watching police officer.

If only it were that simple. Killer or not, anyone would have a 1 in 12 chance of picking the same camera at random. That kind of evidence would never stand up in court.

Or would it? In fact, such probabilistic pitfalls are not limited to crime fiction. “Statistical errors happen astonishingly often,” says Ray Hill, a mathematician at the University of Salford, UK, who has given evidence in several high-profile criminal cases. “I’m always finding examples that go unnoticed in evidence statements.”

The root cause is a sloppiness in analysing odds that can sully justice and even land innocent people in jail. With ever more trials resting on the “certainties” of data such as DNA matches, the problem is becoming more acute. Some mathematicians are calling for the courts to take a crash course in the true significance of the evidence put before them. Their demand: Bayesian justice for all.

That rallying call derives from the work of Thomas Bayes, an 18th-century British mathematician who showed how to calculate conditional probability – the chance of something being true if its truth depends on other …