Your code looks like you want to randomly fill one location with a one, but it has a bias toward the middle. The code below does not.
M=zeros(1,3);
m=randi(numel(M));%pick a random integer between 1 and the number of elements in M
M(m)=1;
%generate the list of positions with a zero
ind_zero=1:numel(M);ind_zero(m)=[];
%randomly pick 1 element from that list
remove_ind=ind_zero(randperm(numel(ind_zero),1));
%remove the element
M(remove_ind)=[];
