Well, you insist there was no communication, but all solutions I can find that yield a probability you describe involve communication. Exemplar being that each

Well, you insist there was no communication, but all solutions I can find that yield a probability you describe involve communication. Exemplar being that each box itself is labeled by a name. Each prisoner starts at the box with their name and reads the slip inside. following a chain of names until they reach their name. The flaw is that this solution violates the premise, the convicts will have knowledge about how the other convicts acted (similar to how they did, otherwise the system fails), which directly violates the premise.