Fitness Proportionate Selection when some fitnesses are 0

I have a question about what to do with the fitnesses (fitness'?) that are 0 when getting the fitness proportionate probabilities. Should the container for the members be sorted by highest fitness first, then do code similar to this:

for all members of population
    sum += fitness of this individual
end for

for all members of population
    probability = sum of probabilities + (fitness / sum)
    sum of probabilities += probability
end for

loop until new population is full
    do this twice
        number = Random between 0 and 1
            for all members of population
                if number > probability but less than next probability then you have been selected
            end for
        end
        create offspring
end loop

My problem that I am seeing as I go through one iteration by hand with randomly generated members is that I have some member's fitness as 0, but when getting the probability of those members, it keeps the same probability as the last non zero member. Is there a way I can separate the non zero probabilities from the zero probabilities? I was thinking that even if I sort based on highest fitness, the last non zero member would have the same probability as the zero probabilities.