The outcome A="At least one" means {1,2,3,4,5......n} where n is the maximum possible outcome.
The only other outcome (B) left (i.e. the complement of the above event "at least one") is (B)={0}.
Therefore, by Kolmogorov's second axiom, A and B are complements, and P(A)+P(B)=1 therefore P(A)=1-P(B), or in words, Probability of outcomes of "at least one" is the complement of the outcome of "0" item.
