Remove --init-path mention

Signed-off-by: Nathan LeClaire <nathan.leclaire@gmail.com>

docs/reference/run.md

@@ -667,18 +667,18 @@ It also causes any seccomp filters to be applied later, after privileges have be
 which may mean you can have a more restrictive set of filters.
 For more details, see the [kernel documentation](https://www.kernel.org/doc/Documentation/prctl/no_new_privs.txt).
 
-## Specifying an init process
+## Specify an init process
 
-You can use the `--init` or `--init-path` flags to specify a process which
-should be used as the PID 1 in the container, and which binary to use for this
-init process, respectively. Specifying an init process ensures the usual
-responsibilties of an init system, such as reaping zombie processes, are
+You can use the `--init` flag to indicate that an init process should be used as
+the PID 1 in the container. Specifying an init process ensures the usual
+responsibilities of an init system, such as reaping zombie processes, are
 performed inside the created container.
 
-The default init process used when specifying `--init` without `--init-path` is
-[tini](https://github.com/krallin/tini).
+The default init process used is the first `docker-init` executable found in the
+system path of the Docker daemon process. This `docker-init` binary, included in
+the default installation, is backed by [tini](https://github.com/krallin/tini).
 
-## Specifying custom cgroups
+## Specify custom cgroups
 
 Using the `--cgroup-parent` flag, you can pass a specific cgroup to run a
 container in. This allows you to create and manage cgroups on their own. You can