With global climate change, extreme weather events such as freezing rain and snowstorms are occurring more frequently, especially in southern China, posing significant risks to power systems. This paper proposes a probability calculation method for conductor breakage in iced distribution lines based on mechanical properties analysis, aiming to assess the risk of conductor breakage under icing conditions. First, a tension model is established to analyze the mechanical behavior of distribution lines under ice and wind loads, calculating both horizontal and vertical tensions and deriving the resultant tension formula. Then, based on reliability theory, a breakage probability model is developed, considering the stochastic variations of ice thickness, wind speed, and line strength. Finally, a case study is conducted to evaluate the probability of conductor breakage under different ice thicknesses and elevation differences, providing effective risk warning references for power utilities.