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As is well known, in quantum mechanics, the calculation rule of theprobability that an eigen-value a_n is observed when the physical quantity A ismeasured for a state described by the state vector |> is P(a_n)=<|A_n><A_n|> .However, in Ref.[1], based on strict logical reasoning and mathematicalcalculation, it has been pointed out, replacing <|A_n><A_n|>, one should use anew rule to calculate P(a_n) for particle satisfying the Dirac equation.  In this paper, we first state some results given by Ref.[1]. And then, wepresent a proof for the new calculation rule of probability according to Diracsea of negative energy particles, hole theory and the principle "the vacuum isnot observable". Finally, we discuss simply the case of particle satisfying theKlein-Gordon equation.

On the calculation rule of probability of relativistic free particle in quantum mechanics