Samuel Rathmanner and Marcus Hutter, "A Philosophical Treatise of Universal Induction" in Entropy 2011, 13, 1076-1136. A very clear philosophical and mathematical analysis of Solomonoff's Theory of Inductive Inference
For a detailed description of Algorithmic Probability, see "Algorithmic Probability"
by Marcus Hutter, Shane Legg, and Paul Vitanyi, in the Scholarpedia,(8):2572.