Contact a professor to agree a research proposal for a post doc position that he is advertising
A postdoc application process is not a competition to find which person can magically understand the PI's objectives, it is there to find the best fit for the job. On the other hand, a postdoc is the start of independent research. You should devise your own research agenda(s) and ask questions about the suitability of your ideas to get a better feel for the project.

In my direct experience and experience of people in a similar position, it is entirely normal to ask questions about the position beforehand. Have a look at the advertisement, it may even explicitly mention to email any questions. My recommendation is to email the PI with a very short description of yourself (research area, where you got your PhD from, etc.) and very short questions. If - this - job is not suitable, the PI may even have you in mind for something else.

In my case I emailed asking if there was scope to do X (there was) for a job in an entirely new field, it is the best position I've ever applied for and I wouldn't have if I had not known it was possible.