Instead, everyone wants an AI solution that automatically separates the important from the fluff. I hate to be a pessimist, but I'm doubtful we'll produce a notable success in this area any time soon, if ever. Priority Inbox certainly isn't it. I spent so much time double-checking its often-wrong results that it made more sense to just stop relying on it.
The unfortunate fact is that the concept of "importance" is vague at best. It differs from person to person, email to email. In many cases, the data that makes an email important can't be found in the inbox at all, and only exists in the real world. If I just met some guy in the hall, and promised that I'd respond to his next email, how will your program take that into account? What about online bank statements, which I normally delete instantly, but which can sometimes be helpful in reminding me to check my account? What about a Facebook message from a girl I find cute vs all the other Facebook messages?
Even humans have a hard time determining the importance of other people's email. Here's a fun experiment: Go through your last 100 emails and write done which ones were important to you. Now have a friend go through the same emails and try to predict which ones you thought were important. You may be surprised at the difference.
The way it deals with your scenario of meeting somebody new and then getting an email from them is that any email sent directly to you from a new person is marked as important.
The way it deals with your second scenario is machine learning. Everyone's priority inbox behaves differently depending on how you train it.