Because P(causation|correlation) > P(causation|~correlation). That is, it's more likely that a causal link exists if you see a correlation than if you don't see a correlation.

Where are you getting this? What are the numerical values of those probabilities?

You can have presence or absence of a correlation between A and B, coexisting with presence or absence of a causal arrow between A and B. All four combinations occur in ordinary, everyday phenomena.

I cannot see how to define, let alone measure, probabilities P(causation|correlation) and P(causation|~correlation) over all possible phenomena.

I also don't know what distinction you intend in other comments in this thread between "correlation" and "real correlation". This is what I understand by "correlation", and there is nothing I would contrast with this and call "real correlation".