Three-body fragmentation of Na-3(+) ions to Na+ + Na(1s) + Na(1s) is studied experimentally and theoretically. A procedure is developed for distinguishing the three adiabatic electronic 1A' states in the product region, even though these states are degenerate at the detector. The procedure requires knowledge only of the three atom-atom and ion-atom relative velocities, and this information is obtained in our coincidence experiments. This paper reports the first experimental determination of the populations of the three-product adiabatic states in a three-body fragmentation process. The results, which are different for each state (despite of degeneracy), are compared with theoretical calculations.