If I missed my probation appointment due to my doctors appointment running late! What will happen? I even have a note from doctor stating I was there! Do I have 24 hours to report before being violated?

That depends on your PO.

They really don't care WHAT your reason is for missing a probation appointment - the only valid reason they will take is if you are dead or in the hospital in critial condition and unable to attend period. Call them as soon as possible and try and explain and tell them you have a doctor's note about it. After they get done laughing (assuming they are normal probation office personnel) you will probably be attending a probation violation hearing in the near future. Doctors appointments second, probation office appointment always FIRST regardless.
If this was a felony probation appointment that you missed - they will not be happy one iota with you. They are going to ask you - why didn't you call? Everyone has a cell phone or telephone in the doctor's office? What were you thinking?

Of course what you did ( I am sure) was to call his office from the doctors office and tell him. Or you went to his office as soon as you got out of the doctors office right?

Got a cell phone, used the phone in the doctors office ?

Ok, if you got a good PO, he will understand and give you a warning,
If you have a jerk as a PO, there may be a warrant out on you right now.