Bernardo randomly picks $3$ distinct numbers from the set $1,2,3,4,5,6,7,8$ and arranges them in descending order to form a $3$-digit number. Silvia randomly picks $3$ distinct numbers from the set $1,2,3,4,5,6,7$ and also arranges them in descending order to form a $3$-digit number. What is the probability that Bernardo's number is larger than Silvia's number?