The statistical indistinguishability of causation from correlation (in non-intervention settings) means that taking all the formal properties of a credence function into account—even the global ones—won’t be enough to distinguish between causation and correlation.

[…] [R]ational credence and rational belief are sensitive to different features of evidence. So while a given body of evidence will usually support a belief just in case it supports a high credence, there is no necessary connection between the two. The statistical cases show that credence doesn’t distinguish between certain facts about our evidence in the way that belief does. What this suggests is the following picture: at the “base level,” we have a body of evidence, which separately determines rational credence and rational belief. Since evidence that supports a high credence is often evidence that supports belief, there is generally a connection between the two. But the in-general connection is not intrinsic; it occurs because of the way both credence and belief are related to evidence, not because of the way they are related to each other.

Lara Buchak, “Belief, Credence, and Norms”