  For a one-locus haploid infinite population with discrete generations, the
celebrated Kingman's model describes the evolution of fitness distributions
under the competition of selection and mutation, with a constant mutation
probability. Letting mutation probabilities vary on generations reflects the
influence of a random environment. This paper generalises Kingman's model by
using a sequence of i.i.d. random mutation probabilities. For any distribution
of the sequence, the weak convergence of fitness distributions to the globally
stable equilibrium for any initial fitness distribution is proved. We define
the condensation of the random model as that almost surely a positive
proportion of the population travels to and condensates on the largest fitness
value. The condensation may occur when selection is more favoured than
mutation. A criterion is given to tell whether the condensation occurs or not.
