How does a Liveness/Readiness probe communicate with a pod?

Short answer: kubelet handle this checks to ensure your service is running, and if not it will be replaced by another container. Kubelet runs in every node of your cluster, you don't need to make any addional configurations.

You don't need to configure a service account to have the probes working, it is a internal process handled by kubernetes.

From Kubernetes documentation:

A Probe is a diagnostic performed periodically by the kubelet on a Container. To perform a diagnostic, the kubelet calls a Handler implemented by the Container. There are three types of handlers:

• ExecAction: Executes a specified command inside the Container. The diagnostic is considered successful if the command exits with a status code of 0.

• TCPSocketAction: Performs a TCP check against the Container’s IP address on a specified port. The diagnostic is considered successful if the port is open.

• HTTPGetAction: Performs an HTTP Get request against the Container’s IP address on a specified port and path. The diagnostic is considered successful if the response has a status code greater than or equal to 200 and less than 400.

Each probe has one of three results:

• Success: The Container passed the diagnostic.
• Failure: The Container failed the diagnostic.
• Unknown: The diagnostic failed, so no action should be taken.

The kubelet can optionally perform and react to three kinds of probes on running Containers:

• livenessProbe: Indicates whether the Container is running. If the liveness probe fails, the kubelet kills the Container, and the Container is subjected to its restart policy. If a Container does not provide a liveness probe, the default state is Success.

• readinessProbe: Indicates whether the Container is ready to service requests. If the readiness probe fails, the endpoints controller removes the Pod’s IP address from the endpoints of all Services that match the Pod. The default state of readiness before the initial delay is Failure. If a Container does not provide a readiness probe, the default state is Success.

• startupProbe: Indicates whether the application within the Container is started. All other probes are disabled if a startup probe is provided, until it succeeds. If the startup probe fails, the kubelet kills the Container, and the Container is subjected to its restart policy. If a Container does not provide a startup probe, the default state is Success.

For network probes, they are run from the kubelet on the node where the pod is running. Exec probes are run via the same mechanism as kubectl exec.