The url-pattern parameter for your servlet (in the web.xml) is independent from the path you specify in your Employee class.
<servlet-mapping>
<servlet-name>ExampleServlet</servlet-name>
<url-pattern>/services/*</url-pattern>
</servlet-mapping>
means your servlet listens on the /services/ sub-path.
@Path("/services/employee")
means that your REST application listens on the /services/employee "sub-sub-path".
So your webservice is exposed at localhost:8080/example/services/services/employee (the concatenation of the url-pattern and the @Path annotation).
If you want to expose it at localhost:8080/example/services/employee with the mentioned url-pattern, you need to change the Employee class needs to have:
@Path("employee")