"Imply X" means "one can logically prove X follows as a consequence." When you say correlation does not imply causation you're saying "there are examples of thi

"Imply X" means "one can logically prove X follows as a consequence." When you say correlation does not imply causation you're saying "there are examples of things which correlate but have no casual relationship." Proving such a claim (by finding an example) is a logical disproof of the claim that correlation implies causation. Logical implication has nothing to do with probabilities in this sense. The point of the article is that correlation (of observed data) does not logically imply correlation (of the underlying phenomena, usually in a more general setting than the data allows).