A Kalman filter (KF) might be used to track targets using measurements from a surveillance sensor. It assumes that measurement noise is uncorrelated, Gaussian, zero mean, with a known variance. Perturbations to target motion are also modelled in a similar way (process noise). These assumptions are only approximately true. In its most basic configuration the variance of both distributions is assumed to be fixed, but in reality is usually variable (depends on the target, target state, sensor state etc). Even though these prior assumptions may be known to hold only approximately, the KF is still used because it gives the desired smoothing behaviour.     

Thanks sir @Hugh for your answer i got that you want to say "That the noise is the main reason for the probability to be unreliable" Is this true?

I assume, the a priori probability is an expectation based on theory. It need not be a match with the empirical probability. If the difference is wide you have to rethink the theory and check the empirical date. If significant difference still exists, reject the theory as not fitting your reality.  

Errors is the noise models certainly increase errors in the target state estimates. Other factors like ambiguity/uncertainty in measurement-to-track assignment also contribute.

Thanks a lot Sir Hugh

There are such  cases where prior info is based on scores given by experts' opinions.  This frequently occurs particularly in social sciences. 

i am new to  Baysian Model can any one just suggest me something from where i can cover just the introduction to  Baysian Model or just comment please thank you...

 Sorry for late sir @Arif, I'am also new to Bayesian model but i recommend you to start from this paper

Take for example the probability of an exam "A" to correctly measure student's performance. Can anyone tell the exact (the physical) probability of the exam?

In well known example of a fair coin, the coin has a physical property that makes the probability of head equals to the probability of tail. In this case, we know the real (the physical) probability and we can test this probability by tossing the coin hundreds of times while counting heads and tails. In classical statistics, they assume that every subject has a physical probability and we should simply get as many samples to reach this physical probability.

Bayesian method didn't move that way. In Bayesian method, we can't say that we reach a physical probability by getting large sample. Instead, we keep accumulating the previous data to the new data. For instance, in exam "A", we keep accumulating the probability of success (correctly measuring students performance) from one test to another.

In general, Bayesian gives us the probability of Model given data is true, but the classical statistics gives us the probability of data given the model is true.