probable cause
US /ˌprɑː.bə.bəl ˈkɑːz/
UK /ˌprɑː.bə.bəl ˈkɑːz/

1.
reasonable grounds (for making a search, pressing a charge, etc.)
:
•
The police had probable cause to search the suspect's car.
•
Without probable cause, the arrest would be illegal.