Problem 67 The problem of the four liars. It is known that each of four people, A, B, C and D, tells the truth in only one case out of three.

Problem 67 The problem of the four liars. It is known that each of four people, A, B, C and D, tells the truth in only one case out of three. Suppose that A makes a statement, and then D says that C says that B says that A was telling the truth. What is the probability that A was actually telling the truth?