Could anyone suggest what test should I apply in the case I have probabilities of 0.

For example, I have a vector of counts 127,2,1,0 and I want to test if this vector fits one of the following probabilities (for example) p1=1,0,0,0 ; p2=0.75,0.25,0,0; p3=0.5,0.25,0.25,0

At first I thought using Chi square goodness of fit, however the I can't have probabilities of 0 and adding some small number (to avoid zeros) seem to mess up the results.

Is there another test or method I could try to determine the original distribution of my counts?

Thanks!