It takes some time (the incubation period ) before a person exposed to rabies develops symptoms. The incubation period for rabies can vary. It can be anywhere from a week to over a year. An incubation period as long as 19 years has been reported. However, it usually lasts about one to three months. The incubation period varies, depending on the amount of virus introduced into the body and the distance the virus has to travel from the site of exposure to the central nervous system (CNS). The closer the bite is to the CNS, the shorter the incubation period. Bites to the head and neck are usually associated with an incubation period of less than one month.
In your case, the chances of developing rabies would be less than one in a billion. There is no role of the vaccine now.