Probability of two candidates that raced each other in an election campaign (Catalan numbers)

213 Views Asked by At

Two candidates A and B raced each other in an election campaign.

Candidate A accumulated $a$ votes and candidate B accumulated $b$ votes.

Assuming $a > b$.

I'm trying to calculate what is the probability that candidate A was leading all the way.

$note:$ I'm thinking maybe it could be Catalan Numbers