How are these notations to be read?

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I came across the following notations in a Software book:

1) $ S(P_0 , ..., P_{n-1} ) $ = ...
2) $ P(i |a,b) = $ ...

First, are these function notations or set notations? I'm assuming they are function notations.

Second, how are they to be read? Here are my guesses...
1) S is a function of variables $ P_0 , ..., P_n-1 $. Is this right?
2) I don't know how to read P. How is this to be read?