A recent report estimated the probability of an earthquake greater than magnitude 7 on the southern section of the San Andreas fault at approximately 60% over the next thirty years. How is that probability calculated?
The probabilities are generally based on long term recurrence rates. You can read about the details in the Working Group on Earthquake Probabilities page Earthquake Probability Models.
The last major earthquake on Southern SAF was in 1857 which means that the average slip deficit on the fault is around ~8.0 m (the Pacific plate is sliding past at a rate of 55 mm/yr). Using empirical scaling laws you can estimate the magnitude of the earthquake that is required to release the accumulated strain. However, the 8.0 m slip deficit is an upper bound as some of the deformation in the region is accommodated by other fault systems, e.g., Elsinore and San Jacinto faults (sub-parallel to SAF) as well as the Eastern California Shear Zone which was the site of Landers/Hector Mine earthquakes in the 90s.