The authors present a class of normal modal calculi \(P_ FD\), whose syntax is endowed with operators \(M_ r\) (and their duals \(L_ r)\) one for each \(r\in [0,1]\). If a is a sentence, \(M_ ra\) denotes ``the probability that a is true is strictly greater than r'', and to be evaluated as true of false in every word of an F-restricted probabilistic Kripke model. Every model of this type is a Kripke model with a family of regular probability evaluations with range in a finite subset F of [0,1]. In this case, there is one such function for every world w, i.e. \(P_ F(w,-),\) and this allows to evaluate \(M_ ra\) as rue in the world w if and only if \(P_ F(w,a)>r\). The authors give axioms and rules and show that the resulting system \(P_ FD\) is complete and compact with respect to the class of all the F-restricted probabilistic Kripke models. The paper is concerned with the problem to which extent statements like ``a is possible'' and ``a has a probability strictly greater than zero to be true in a conceivable state of affairs'' can fit. The authors claim that their paper is the very beginning of a work that can be pursued. The reviewer hopes that they will examine the problem thoroughly.