Schneidman-Duhovny D, Hammel M, Tainer JA, Sali A (2013) Accurate SAXS Profile Computation and its Assessment by Contrast Variation Experiments. Biophysical Journal 105:962–974.
P(r) is simply the Fourier transform of q^2*I(q). It includes the hydration layer.
It is not usually normalized and is equal to the 4pi r^2 weighted probability of finding electrons a distance r apart. It is also a histogram of the number of all possible electron pairs.
The integral of P(r) is I(0). So that should be the normalization you seek. It is reported in the GUI when you compute a P(r) function.
The best description I have found of P(r) can be found in this reference:
Glatter, O. The Inverse Scattering Problem in Small-Angle Scattering. in Neutrons,
X-Rays, and Light: Scattring Methodds Applied to Soft Condensed Matter (2002).
Hope this helps.