The title is a typical example of "transposing the conditional". What they mean is P(observations|local realism) < 10^-9, but what they wrote is P(local realism

The title is a typical example of "transposing the conditional". What they mean is P(observations|local realism) < 10^-9, but what they wrote is P(local realism|observations) < 10^-9. Science publications should know better!