Feel bad for applying to two postdoc positions

I'm a finishing PhD student in math. I want to stay in academia so I am applying for two things:

1. A year-long postdoc position


2. A 6 month postdoc position

I have been in contact with two professors regarding the two options and am going to send the application forms off today. But I feel bad because suppose I get job offers for both the positions, then I'll have to say no to one of them. Then they will get annoyed at me for wasting their time and will probably never want to work with me on anything again. Both are highly respected so it's doubly bad. What should I do?