Multinomial probabilty


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?



Less is more. Stay pure. Stay poor.
Can you tell us a little bit more for what this is for or the origins of data? So their is a vector 1 with n values and other vectors of the same size for which you want to match the best fit.

I guess my question is where the other vectors came from and what do they represent? Not knowing more about these data limits recommendations.