Guessing Quantum Ensemble Using Laplace Principle

For a mixed quantum state with density matrix $\rho$ there are infinitely many ensembles of pure quantum states, which average to $\rho$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any particular state), we derive a `natural' distribution of pure states averaging to $\rho$, which is `more spread' than all the others.