Leading candidate never trailing in a 100 to 80 count

In an election candidate $A$ receives $n$ votes and candidate $B$ receives $m<n$. The ballots are shuffled and counted one at a time, with a running total for each. Let $Q(n,m)$ be the probability that $A$'s running total is never below $B$'s at any point after counting begins (ties are allowed). Compute $Q(100,80)$.

$21/101$. All orderings are equally likely, so count lattice paths. A path is bad iff it touches the line where $B$ leads by one; reflecting the part up to the first touch gives a bijection with all paths to a shifted endpoint, so $Q(n,m)=1-\tfrac{m}{n+1}=\tfrac{n+1-m}{n+1}$. Here that is $\tfrac{21}{101}$.