A legally recognized relationship of interest of two parties, be it in a transaction, a piece of property, or a proceeding. horizontal privity. The legal relationship between two parties in a distribution chain who are on equal level, as between two consumers. See also vertical privity. privity of contract. The relationship between the two parties to a contract that confers a right to take action on the contract; largely abrogated by enactment of warranty laws, permitting suits by users of pr...