In this paper I want to outline how the sequential logic introduced in [12] can serve as a syntactical basis for a non-classical modal logic. In a second step I shall found a probability theory on this modal logic in such a way that probabilities represent degrees of possibility. The three levels: sequen? tial logic, modal logic, probability theory, are connected as follows: (a) The sequential logic is represented by an algebra of projections in a complex Hubert space H. These projections (or their ranges) are the ele? mentary events or yes-no propositions of the calculus which contains, with two propositions W9 P also events like WnP9 read "Wand then P", and W-* P9 read "if (first) Wthen P". If this last conditional is true, i.e., if W P is all of H9 we say that P is logically implied (entailed by W9 symbolically W < P. This < coincides with the partial order of inclusion of subspaces of H. (b) The necessity operator Nw with respect to a fixed event W is given by NWP: = W -+ P9 i.e., Nw maps P onto the conditional W-+ P9 and we call P W-necessary if the image of P under Nw is H: P is Unnecessary if and only if P is logically entailed by W. The possibility operator Mw is derived from Nw in the usual manner: MWP: = (NwP1)1, where orthocomple mentation x represents negation. It turns out that P is ^-possible exactly if Wr\ P is not identically 0 ( = zero projection) which latter represents fal? sity. (c) W n P # 0 is equivalent to PWP ^ 0. PWP is the so-called con? ditional probability operator for the probability of P on the condition that the system is in the (pure) state W ( = projection of rank 1). It is shown, first by an intuitive argument, and then by way of requiring a minimal set of two Kolmogorov-type axioms that prob^CP) := <