  The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov
complexity with the discrete universal distribution. There are conditional
versions referred to in several publications but as yet there exist no written
proofs in English. Here we provide those proofs. They use a different
definition than the standard one for the conditional version of the discrete
universal distribution. Under the classic definition of conditional
probability, there is no conditional version of the Coding Theorem.
