Effect of Normalization On a Distribution

Question

Let's assume that we have calculated some values proportional to probabilities for a special distribution(some hypothetical distribution other than normal distribution but we don't know which distribution it is). I want to use those calculated values as the probability densities for the distribution. To make the sum of probabilities equal to one, I normalize the calculated values (dividing each by sum of all). Would I lose the actual character of the distribution by doing this normalization. Because the name 'normalization' suggests that it would make the final distribution a normal distribution.