In which case was probable cause established as a requirement for arrests?

Probable cause being established as a requirement for arrests directly relates to Illinois v. Gates. In this landmark decision, the U.S. Supreme Court established the "totality of the circumstances" standard for evaluating probable cause in the context of search and seizure. The Court determined that a warrant could be issued based on a combination of factors, rather than strict adherence to previously established standards. This case was significant in clarifying that law enforcement officers must have a reasonable belief that a crime has been committed or that evidence related to a crime can be found in a certain location before making an arrest or conducting a search.

The other cases mentioned focus on different aspects of the law: Miranda v. Arizona is known for establishing the requirement of informing suspects of their rights during an arrest, Terry v. Ohio involves "stop and frisk" regulations, and Roe v. Wade is centered around reproductive rights and privacy rather than issues of probable cause in arrests.