When I get a cold I pray to Zeus. It always clears up in a few days. Can't think of any other reason for it getting better, therefore by your 3 criteria I'm justified in thinking Zeus cures my colds.

Actually, to establish causation, in as much as this is possible at all [1], you need a predictive model and controlled experiments.

[1] following Hume, you can never definitively show causation.