Not necessarily possible even with the private keys. If you use an SSL cipher with ephemeral keys, such as the DHE_* or ECDHE_* family of ciphers, then an eavesdropper with a recorded but not MITMed conversation cannot decrypt it even with the server's private SSL key.
Which of course they do not. Google uses ECDHE_RSA. DDG uses RSA. ixquick, "the world's most private search engine", uses RSA. Bing does not even offer https.
Google does pin their keys in Chrome though, so they know if there is a MITM (and they have, Chrome's certificate pinning led to DigiNotar's downfall). It's a non-scalable hack, but definitely a good one for the largest search engine and a leading email provider to be able to provide.