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buybuydandavis comments on Causation, Probability and Objectivity - Less Wrong
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Which can be represented in a straightforward fashion in Jaynes's notation.
f(y | x0, x1=C... xN=C2)
If x "is a cause" of y when x1...xN, then this conditional will accurately predict y without ever saying "cause". The causal talk seems to me superfluous mathematically - it's just describing limiting cases of conditionals.
If you literally think that conditional probabilities describe causation, then you should water your grass to make it rain (because p(rain | grass-is-wet) is higher than p(rain | grass-is-dry)). Causation is not about prediction.