In this paper, we present the relationship between the pri- vacy definition for Radio Frequency Identification (RFID) authentication protocol. The security model is necessary to ensure the security or pri- vacy, but many researchers describe different privacy notion for RFID authentication and the technical relationship among them is unclear. We reconsider the zero-knowledge privacy proposed by Deng et al. in ESORICS 2010 and show that this privacy is equivalent to the indis- tinguishability based privacy proposed by Juels and Weis. Furthermore, we present that these privacy definitions are technically weaker than the simulation based privacy proposed by Paise and Vaudenay in AsiaCCS 2008.