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](https://en.wikipedia.org/wiki/Elo_rating_system#Mathematical_details):

> If Player A has a rating of R<sub>A</sub> and Player B a rating of R<sub>B</sub>, the exact formula [(using the logistic curve)](https://en.wikipedia.org/wiki/Logistic_curve) for the expected score of Player A is 
>  
> E<sub>A</sub> = 1 / (1 + 10 <sup>(R<sub>B</sub> - R<sub>A</sub>) / 400</sup>)

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 E<sub>A</sub> = 0.6294.