Mplus prints estimates of [c#1 c#2...]; that is the logits corresponding to the intercepts/means of the multinomial regression on covariates (no covs implies that the intercepts are the means). Then use UG Chapter 14 formulas on pages 441-445 to translate from those logits to probabilities.
Sorry I should have looked into this more closely before posting. It seems that the SEs for the results in probability scale can be obtained using the delta method and the output in TECH3. Thanks, Peter