 The idea is thus that the agent probability of \(B\) conditional on \(A\) is the probability that \(B\) would have conditional on the assumption that \(A\) has a special sort of status or history—in particular, on the assumption that A is realized by a free act. \(A\) will be a cause of \(B\) just in case the probability of \(B\) conditional on the assumption that \(A\) is realized by a free act is greater than the unconditional probability of \(B\); \(A\) will be a spurious cause of \(B\) just in case these two probabilities are equal. As an illustration, consider a stock example of philosophers—a structure in which atmospheric pressure, represented by a variable \(Z\), is a common cause of the reading \(X\) of a barometer and the occurrence of a storm \(Y\), with no causal relationship between \(X\) and \(Y. X\) and \(Y\) will be correlated, but Price’s and Menzies’ intuitive idea is that conditional on the realization of \(X\) by a free act, this correlation will disappear, indicating that the correlation between \(X\) and \(Y\) is spurious and does not reflect a causal connection from \(X\) to \(Y\). If, by contrast, this correlation were to persist, this would be an indication that \(X\) was after all a cause of \(Y\). (What “free act” might mean in this context will be explored below, but I take it that what is intended—as opposed to what Price and Menzies actually say—is that the manipulation of \(X\) should satisfy the conditions we would associate with an ideal experiment designed to determine whether \(X\) causes \(Y\)—thus, for example, the experimenter should manipulate the position of the barometer dial in a way that is independent of the atmospheric pressure \(Z\), perhaps by setting its value after consulting the output of some randomizing device.)