If you are an employee of a business and send out email on the business' computers under most state laws it has the right to go to the computer and access all the contents, including the emails. Most employers publish that in their handbooks for additional protection.
It normally requires a search warrant for the police to gain access to your private email (say at home on a personal PC -- in the office the firm can give permission). A private investigator has NO right to access your email, unless you, or someone else who has a right to access it, gives permission. Period.
However, generally anyone to whom you send an email may share it with anyone else.
