The degree of progress to goal at any stage during self-organization process was considered in Olatinwo [8]. The transition probabilities at various time intervals(including initial and final times) were evaluated and then subsequently interpreted as the degrees of progress to goal at such time intervals. The distance function employed in that paper was time-dependent of explicit form, contained in Adeagbo-Sheikh [1]. In this paper, we generalize the results of Olatinwo [8] by considering a distance function which is an implicit function of time. We apply both the notions of Jensen's inequality and triangle inequality as well as the elementary ideas of the convex functions and the curve theory.\par The results obtained are in agreement with the axiomatic properties of probability.