#Matlab, 83, 77, 71 Bytes
function a=x(a)
if~nnz(a-a(1));a=[a,1];else[~,I]=min(a);a(I)=a(I)+1;end
I'm relatively new to code golf so please be kind! I tried to use anonymous functions but googling says you can't use if/else statements and matlab doesn't have ternary operators, so this is the best i felt I could do.
Edit: Corrected and shortened (twice!) thanks to stewie-griffin.