  We complete the task of optimal probabilistic coherence distillation
protocol, whose aim is to transform a general state into a set of n-level
maximally coherent states via strictly incoherent operations (SIO).
Specifically, we present the necessary and sufficient condition for the
transformation from a mixed state into a pure-state ensemble via SIO. With the
aid of this condition and the simplex algorithm, we can accomplish the
probabilistic distillation protocol by presenting an analytical expression of
the maximal average distillable coherence of a general state and constructing
the corresponding operation achieving this bound. Our protocol is a universal
protocol since it can be applied to any coherence measure.
