An officer's personal knowledge of a suspect's past would be considered more likely to establish probable cause than just knowing they had a rap sheet. In most cases, however, knowledge of this information is considered by the law to be relevant, but not sufficient. This is, again, a presumption. Innocent people would react more strongly to various police actions that are incriminating. It definitely cannot be used alone as a basis of probable cause, but the interesting thing about it is that the police have it both ways.
Hearsay is any second-hand information.
The most common situation involves informants. A two-prong test requiring the affidavit spell out the underlying circumstances of how the informant gained their knowledge AND a statement of the informant's veracity, or record of truthfulness. A three-prong test requiring all the elements of Aguilar plus an assessment of how accurate the information from the informant might be from a police perspective. Between the Police Officer and the Magistrate .