kill -0 tests if you may send a signal to the target process. If you are not the owner of the process or root, the answer will always be "no".
If you have the PID and just want to know if the process exists or not, you should use the ps command with the -p option. If you want only the information about the existence of the process, throw the ps output away and use only the result code returned by the ps command.
Example:
#!/bin/sh
pid=1 # or whatever
if ps -p $pid >/dev/null; then
echo "process $pid exists"
else
echo "process $pid does not exist"
fi
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