It's basically just table 8.1a with the columns switched. E.g. the entry in table 8.1b with rating difference 92-98 and expected score (for the higher rated player) of .63, corresponds with the entry (.63, 95) in table 8.1a.
That table is based on the expected score formula mentioned here:
If Player A has a rating of RA and Player B a rating of RB, the exact formula (using the logistic curve) for the expected score of Player A is
EA = 1 / (1 + 10 (RB - RA) / 400)
but it's also possible to directly generate table 8.1b from this formula. For example, a rating difference of 92 points (in A's favor) leads to EA = 0.6294.
The inverse formula, calculating the rating difference which corresponds to a certain expected score, is RB - RA = 400 log10(1 / EA - 1).