What are the chances of getting that disease after getting the vaccination?

Possibly, but not as bad as if you were not vaccinated.

Vaccination is an injection of the disease you wish not to catch. This is done so your body will develop the needed, reactive antibodies to the disease in question. The injected form of the disease has been modified so that it is not as powerful and won't do as much damage as the one you are preventing, but reactions in people differ and reactions to this inoculations will include the symptoms of the disease.

The chances of a reaction depend on the person who is injected. When you get a cold does it hit you hard and you are down for awhile? That might be an indication of how your internal protection system works and you should prepare yourself for experiencing the symptoms of the vaccine.