Bertrand's ballot theorem

Bertrand's ballot theorem is a result in combinatorics related to voting and elections. It can be stated as follows: Suppose that in an election, candidate A receives \( a \) votes and candidate B receives \( b \) votes, with \( a > b \). If the votes are counted one by one in a random order, the probability that candidate A is always ahead in the vote count throughout the counting process (i.e.