Final answer:
There is no specific Supreme Court case provided that established the role of a suspect's criminal record in satisfying probable cause. However, Illinois v. Gates and Terry v. Ohio both offer important insights into the standard of probable cause under the Fourth Amendment.
Step-by-step explanation:
The Supreme Court case that established whether an officer's knowledge of a suspect's criminal record may be enough to satisfy probable cause is not specified in the materials provided. However, Illinois v. Gates set an important precedent concerning probable cause by establishing the "totality of circumstances" test under the Fourth Amendment, which allows for a more flexible assessment of whether there is a sufficient basis to take action based on probable cause.
The relevant Supreme Court decision about probable cause not specifically mentioned in the provided materials, but Terry v. Ohio is an example of a case that discussed the threshold for when officers may stop and frisk a person based on reasonable suspicion, a concept related to probable cause. Additionally, Mapp v. Ohio addressed the exclusionary rule that prevents evidence obtained without a warrant, or not fitting within an exception to the warrant requirement, from being used in a state criminal trial. This case helps define what happens when probable cause is lacking for a search or seizure.