We address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of $M$ which are invariant under the natural action of $\operatorname{Aut}(M)$. This pursuit requires a generalization of Shelah's forking formulas [8] to "essentially measure zero" sets and an application of Myer's "rank diagram" [5] of the Boolean algebra under consideration. The classification is completed for a large class of $\aleph_0$-categorical structures without the independence property including those which are stable.