Final answer:
Analytical procedures are least likely to disclose related party transactions as they do not focus specifically on identifying such transactions compared to more direct methods like confirmation of balances, reviewing contracts, or inquiries with management.
Step-by-step explanation:
The audit procedure that would be least likely to disclose the existence of related party transactions of a client during the period under audit is analytical procedures comparing current year transactions with prior years (Option 3).
While confirmation of balances with related parties, review of contracts and agreements, and inquiries of management are direct approaches specifically targeting related party transactions, analytical procedures are more general and might not specifically identify transactions with related parties unless there are significant deviations from expected trends or ratios that warrant further investigation.