The paper is a good reference to personalized page rank. Basically my understanding, ppr scores tell you the probability from the source node move to the target node. It is a specific score describe the relationship between specific source and target nodes in the graph.
If you have problem to reproduce the results, you can use networkx in python, load a graph and compute ppr using
networkx.pagerank(graph, personalization={'a':0, 's':1, 'b':0....})
Networkx use power iteration approach to compute ppr, you can get exact result as what shown in the example.
The author of this thesis have c++ code here https://github.com/snap-stanford/snap/blob/master/snap-core/randwalk.h Since this method is random walk based approach, you could not get exactly same results as what shown in the example, but the rank is correct.
Hope that helps.