The most expensive railway in Japan is the Hokuso Line, which runs for a mere 32.3 km between the Keisei Takasago Station in eastern Tokyo and the Inba Nihon Idai Station in Chiba Prefecture. If you travel from one end of the line to the other it takes 34 minutes and costs ¥870, which comes out to about ¥27 per kilometer.
Of course, many factors go into determining train fares and most of them have to do with the local situation. The main factor is demand, which is why you usually find higher fares in the deep countryside, where the sparse population can't always support regular railway service. However, the Hokuso Line connects a fairly well-populated section of western Chiba to the capital via the Keisei and Keikyu railways, so why is it so much more expensive that other lines in the area?