Distribution of distance between eigenvalues for GOE when $n=2$

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This question is a possible duplicate of PDF of the Difference of Eigenvalues of a GOE

I was reading Introduction to Random Matrices Theory and Practice by Giacomo Livan, Marcel Novaes, Pierpaolo Vivo.

Appetizer: Wigner’s surmise

I don't understand how he reaches 2.2 (in the attached image) by "definition". Could you provide some reference or tell me exactly what definition is he using? Why is $p(s)$ equal to the original joint pdf "tested" against a Dirac Delta?