The probabilistic top-k queries based on the interplay of score and probability, under the possible worlds semantic, become an important research issue that considers both score and uncertainty on the same basis. In the literature, many different probabilistic top-k queries are proposed. Almost all of them need to compute the probability of a tuple t_i to be ranked at the j-th position across the entire set of possible worlds. The cost of such computing is the dominant cost and is known as O(kn^2), where n is the size of dataset. In this paper, we propose a new novel algorithm that computes such probability in O(kn).