The failure probability of a pipeline is a quantification of the likelihood of an accident occurring in the pipeline, which is an indispensable part of the pipeline risk assessment process. To solve the problems of strong subjectivity, low feasibility, and low accuracy in the existing pipeline failure probability calculation methods, a three-layer Bayesian network topology model of “pipeline failure–failure cause–influencing factor” is proposed, with the pipeline failure as the subnode, the type of pipeline failure as the intermediate node, and the factors affecting the pipeline failure as the parent node of the network. Based on data fitting and fuzzy theory analysis methods, the functional relationship between the impact factor and the failure frequency of various pipelines is quantified. Using the mean value theorems for definite integrals and the analytic hierarchy process, the conditional probability of the directed edge in the network is calculated. The proposed function relationship provides a method to calculate the prior probability according to the parameters of the pipeline and its surroundings and a new idea to train the network model even without sufficient data.