What is the estimated population of snow leopards in the world today?

There are approximately 3,500 to 6,500 in the wild. In addition, there are 600-700 snow leopards in zoos around the world.
From 4500 to 6000. Snow Leopard Trust. (N.A). SNOW LEOPARD FACT SHEET. Retrieved 04 22, 2012.

11% (about 600) out of all snow leopards live in zoos.