So, when they try to justify trespassing on someone's email account
Which is a service provided by them. Hosted on their servers. Stored on their servers. Wait, which part of this was trespassing?
Reading. Unless they somehow actually moved the bits of the e-mail out of the person's account, and into theirs. Even if they made a copy, it's not stealing.
by saying that they had "probable cause to believe" whatever, it doesn't fly
Why doesn't it, though? And in what sense? A moral sense, a business internal rules and regulations sense, a legal sense?
Maybe I should go break into my neighbor's house in the middle of the night and ransack the place because I have probable cause to believe he "borrowed" my week whacker without asking... that'd be perfectly okay, right Microsoft?
Horrible analogy. What if your neighbor came into your house each night, with your permission of course, you told them that they can use your computer all they like without fear of you peeking of their shoulder as it were, as long as they don't start downloading a bunch of movies, and that you reserve the right to check their internet activity if you believe they did - then find that your internet usage surged and you kept hearing the 20th Century Fox, Universal and other well-known studio themes?
Would you then, as per your own stipulation, check whether maybe they did download a whole bunch of movies - even though the person may have just been downloading Linux distros and playing those studio themes on youtube because they're a fan of movie studio themes?
If no: Why not?
If yes: How bad would you feel about doing so?
While it's all good and well to think our stuff at third parties is private - and in some cases some laws may even agree with you to an extent - I think we're all aware that in practice, anybody can be looking in.. and when the subject of the material is the proprietor of the service, doubly so.