Do you think it is literally equally likely that causation exists if you observe a correlation, and if you don't?

I think I have no way of assigning numbers to the quantities P(causation|correlation) and P(causation|~correlation) assessed over all examples of pairs of variables. If you do, tell me what numbers you get.

I assert that, intuitively, the former seems likely to be greater.

I asked why and you have said "intuition", which means that you don't know why.

My belief is different, but I also know why I hold it. Leaping from correlation to causation is never justified without reasons other than the correlation itself, reasons specific to the particular quantities being studied. Examples such as the one you just linked to illustrate why. There is no end of correlations that exist without a causal arrow between the two quantities. Merely observing a correlation tells you nothing about whether such an arrow exists. For what it's worth, I believe that is in accordance with the views of statisticians generally. If you want to overturn basic knowledge in statistics, you will need a lot more than a pronouncement of your intuition.

By "real correlation" I mean a correlation that is not simply an artifact of your statistical analysis, but is actually "present in the data", so to speak.

A correlation (or any other measure of statistical dependence) is something computed from the data. There is no such thing as a correlation not "present in the data".

What I think you mean by a "real correlation" seems to be an actual causal link, but that reduces your claim that "real correlation" implies causation to a tautology. What observations would you undertake to determine whether a correlation is, in your terms, a "real" correlation?