For some problems in distributed hash table (DHT), it is insufficient to show the virtue of algorithm only with the notation. The paper gives two groups of the elementary probability distribution on the discrete and continuous address spaces. With these properties, the paper analyzes two problems of the load balance and estimation of the network size in DHT, and obtains such results: the loads of nodes in Chord network are imbalanced; and Pastry adopts the half of the interval between two neighbor nodes as the managed zone, which makes great improvement on the balance; moreover the problem of estimating the size of network is equivalent to the problem of estimating the parameter of a passion process.
