Courts don't bother themselves with confidence intervals nor do they bother with 100% ("reasonable doubt" is not 0/100%).

The problem is the current situation. Evidence is being used without actual proof that said evidence was collected "truthfully". An algorithm will generate a result but if you haven't proven/shown that the algorithm generates a correct result then any result from that algorithm shouldn't be usable in court. This problem comes up a lot with people who (un)cleverly use NULL for things (i.e. License Plates). Or if you live in the middle of America and somebody decides your address will be the default for geo-ip lookups if none is found.

To stick with the article, immediately when the system was deployed the postmasters thought something was wrong. If the state had to show that the computer was correct the whole situation would've been avoided.

No sudden unexplainable wealth, no bank transactions to personal accounts, no incriminating text messages. Even if the code was correct that alone is not proof the individuals accused took the money, but they were still convicted. That isn’t supposed to happen.

For the postmaster example, they did show it to be correct at their accepted level of confidence. Which is that it returns superficially believable results.

100% correctness for such a system would certainly cost many billions.

If you mean that they should have had a higher bar, then sure, but that's a political choice of how much effort to invest, not a technical one.

Is any aspect of any legal system anywhere based on 100% confidence?