Confidentiality, integrity, and availability or the CIA triad of security

Confidentiality, integrity, and availability or the CIA triad of security is introduced in this session. These three dimensions of security may often conflict. Confidentiality and integrity often limit availability.  So, a system should provide only what is truly needed. This means that a security expert has to carefully analyze what is more important among these three dimensions of security in a system or application. 

Please provide an example (and justification) where the confidentiality of a system is more important than the integrity or availability of that system. Then provide an example where the integrity of a system is more important than the confidentiality or availability of that system. Finally, provide an example of a system where the availability of a system is more important than the confidentiality or integrity of that system. For example, you might say availability is more important than integrity and confidentiality in a cell telephone system since one must be able to reach their loved ones in an emergency. Someone else might argue confidentiality/privacy is more important in such a system.