How can a female snake have baby without its mate specially in zoos?

Hi,
This is a phenomenon called parthenogenesis. It has been observed in many animals including some snakes. You can read more about it here: http://en.wikipedia.org/wiki/Parthenogenesis.
Usually when this happens, the female produces an egg that develops into an embryo without being fertilized by sperm. Because the embryo does not possess any chromosomes from a male parent, it will usually be a genetic clone of the mother.