The causation does exist but in a different direction (see the GP's post about storks and chimneys).

GP's post was about storks on houses.

This article studies the number of storks in a country overall.

So it's not really related. I'd say total storks in a country and total births in a country are more related to the size of the country.

Is there a formal notation for always or usually?

Yes, P(correlation ∩ causation) = 1 would be textually written as "It is almost certain that correlation and causation occur together". Or to bring you closer to the example, you could say P(causation | correlation) = 1 to say "It is almost certain that causation exists if correlation exists".

You can alter the right-hand side, but then you have to stop saying 'almost certain' because everyone assumes that means a measure one set.

So, for instance, you might believe that P(causation | correlation) = 0.8 across all human chosen distributions. You might well be right since adversarial distributions are so rarely chosen, i.e. there is a meta-effect where humans are choosing interesting queries in the first place.