#### Answer

$$\frac{365\cdot364\cdot363\cdot362}{365^4}$$

#### Work Step by Step

Whenever one person has a birthday, there is one less day in the year that could be a different birthday. Thus, we multiply 365/365 by 364/365. We continue this trend for the given number of people that there are. So, for four people, we find:
$$\frac{365\cdot364\cdot363\cdot362}{365^4}$$