3 years before I exchanged email with a professor for Ph.D program. He sent me several links including the process of his university for PhD and some useful links, in the meanwhile I also contacted to another professor in another country. I selected the second option to continue my PhD. Now I completed my PhD. Is it ethical to send email and ask the first professor for postdoc position?
Yes, of course. Your earlier decision doesn't reflect at all on either of you as you had a variety of criteria for choosing. You don't need to defend that decision in any way. The prof in question was interested in you at one time and may still be interested.
The professors needs may have changed, of course. But if you apply you an even remind him/her of your earlier exchange, providing thanks for the earlier guidance. Of course, make sure that you have some knowledge of the potential position and the work of the professor and how you can contribute to it effectively.
There is no ethical issue and while there might be cultural issues in a few places, one hopes that those are minor in the modern world.