Even with a perfect model there exist states that are indistinguishable given any amount of previous observations if there is any error in the observations. These indistinguishable states are easily computed given a shadowing trajectory. The concept easily generalizes to situations with imperfect models. The ideal ensemble for probabilistic forecasting is a random sample of indistinguishable states. The principles are illustrated using the Navy Operational Global Atmosphere System NOGAPS. We may also discuss targeted observations from a indistinguishable states perspective.