Outlier detection over sliding window is a fundamental problem in the domain of streaming data management, which has been studied over 10 years. The key of supporting outlier detection is to construct a neighbour-list for each object. It is used for predicting which objects may become outliers or are impossible to become outliers. However, existing work ignores the fact that, outliers amount is usually small. It is unnecessary to construct neighbour-list for all objects when they arrive in the window. It causes both high space and computational cost, can not efficiently work under edge computation environment. In this paper, we propose a novel framework named PTAOD (Probabilistic Threshold-based Approximate Outlier Detection). Firstly, we propose an algorithm for evaluating the probability of a newly arrived object becoming an outlier before it expires from the window, using evaluating result for avoiding unnecessary computational cost. In addition, we introduce a novel index namely ZHB-Tree (Z-order-based Hash BTree) to maintain streaming data. Last of all, we propose a novel algorithm to maintain candidate outliers. Theoretical analysis and extensive experimental results demonstrate the effectiveness of the proposed algorithms