This paper focuses on processing continuous k nearest neighbor queries over objects moving at uncertain speeds (CUkNN) in road networks. We present a novel model to estimate the distances between objects and a query, both of which move at variable speeds in the road network. Based on the proposed distance model, we present a CUkNN query monitoring method to continuously find the objects that could potentially be the k-nearest neighbors (kNN) of the query. We propose an efficient method to calculate the probability of each object being a kNN of a query. The key thing about the method is that the probability of an object being a kNN of query q is shown to be equivalent to the probability of a special line segment being one of the k-nearest lines from q, which greatly simplifies the probability calculation.