How to Find the Probability of Kalman Filter States?
The idea of Kalman is it fuses the data with the optimal weighing to get results.
Optimal requires definition and in the case of Kalman it means that if your model is right this is the optimal.

Since we operate Kalman filter under the assumption the model is right no Kalman Filter will allow you doing what you want.

Now, it seems that in your case what you don't like is the transient phase when there are low number of measurements.
What I can suggest is that for this start phase you will built your own filter based on your weighing and after few iterations send your result to the Kalman Filter as a starting point.