Opinion formation in the population has attracted extensive research interest. Various models have been introduced and studied, including the ones with individuals' free will allowing them to change their opinions. Such models, however, have not taken into account the fact that individuals with different opinions may have different levels of loyalty, and consequently, different probabilities of changing their opinions. In this work, we study on how the non-uniform distribution of the opinion changing probability may affect the final state of opinion distribution. By simulating a few different cases with different symmetric and asymmetric non-uniform patterns of opinion changing probabilities, we demonstrate the significant effects that the different loyalty levels of different opinions have on the final state of the opinion distribution.