If I make profit by scan a book for someone who already owns them, will it be illegal?

Yes, the copying will be copyright infringement. See Intellectual Property counsel.

This is copyright infringement. The website that do similar things either have a license or fall under fair use because they are allowing the work to be indexed, akin to a card catalog in a library.

Look, to be pragmatic, in your case no one is ever going to know or care about you scanning one book. But if this was a proposed business venture, you probably have some serious flaws because you would not be entitled to make copies. As my colleague notes, there may be some aspects that invoke fair use here, but that would have to be explored. Further, fair use is a legal defense and the copyright holder is always free to drag you into court and force you to prove out your use as fair. So if you plan on relying on that defense you better be right and that rightness better be obvious. I suggest that you consult with a lawyer in private and discuss your objectives in more detail. You can start by calling around to several for a free phone consultation, get some insights then pick the best fit to work with. Best regards, Frank Natoli-Lapin, LLC

What you propose is most likely copyright infringement. The owner of any particular copy of a book does not typically also own the right to make copies of that book, and therefore cannot give you license to make any copies either. Only the actual holder of the copyright (e.g., the author, or the company for whom the author produced the work) can give you permission to make electronic copies. Although some unauthorized copying is considered to be a "fair use" of another's content, it is unlikely that this scenario would be considered a fair use. You may wish to consult with an IP attorney before proceeding with a business model that is based on copying copyrighted materials.