The global zone and each kernel zone manage their own process ID space. The same numeric process ID might identify different system processes in the global zone and in one or more kernel zones. For example, on the same physical host, you can have the numeric process 5678 running syslogd on the global zone and running sendmail on a kernel zone.
To kill process 5678 with the ps command in kzone1, use the zlogin command followed by the kill command.
global# zlogin kzone1 kill 5678