I am in a state probation. Can I have a passport to travel abroad?

Most likely NO. You will have to wait till you are off probation before you are allowed to visit another state, little lone another country.

Besides, if you have a record (felony) the country you wish to visit MAY refuse you a visa. Being off probation, I can probably visit Australia, but if I want to move there, AIN'T HAPPENING.

You will have to ask your probation officer cause you probably will be able to get your passport and fly but on your way back they may arrest you if you travel without your probation officer approval.