  As is well known, in quantum mechanics, the calculation rule of the
probability that an eigen-value a_n is observed when the physical quantity A is
measured 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 mathematical
calculation, it has been pointed out, replacing <|A_n><A_n|>, one should use a
new 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, we
present a proof for the new calculation rule of probability according to Dirac
sea of negative energy particles, hole theory and the principle "the vacuum is
not observable". Finally, we discuss simply the case of particle satisfying the
Klein-Gordon equation.
