Improve explanation of failureThreshold for Pod probes (#37416)

* Update configure-liveness-readiness-startup-probes.md

* Update content/en/docs/tasks/configure-pod-container/configure-liveness-readiness-startup-probes.md

Co-authored-by: Tim Bannister <[email protected]>

Co-authored-by: Tim Bannister <[email protected]>

Author: LouisJULIEN

content/en/docs/tasks/configure-pod-container/configure-liveness-readiness-startup-probes.md

@@ -388,9 +388,24 @@ to 1 second. Minimum value is 1.
 * `successThreshold`: Minimum consecutive successes for the probe to be
 considered successful after having failed. Defaults to 1. Must be 1 for liveness
 and startup Probes. Minimum value is 1.
-* `failureThreshold`: When a probe fails, Kubernetes will
-try `failureThreshold` times before giving up. Giving up in case of liveness probe means restarting the container. In case of readiness probe the Pod will be marked Unready.
-Defaults to 3. Minimum value is 1.
+* `failureThreshold`: After a probe fails `failureThreshold` times in a row, Kubernetes
+  considers that the overall check has failed: the container is _not_ ready / healthy /
+  live.
+  For the case of a startup or liveness probe, if at least `failureThreshold` probes have
+  failed, Kubernetes treats the container as unhealthy and triggers a restart for that
+  specific container. The kubelet takes the setting of `terminationGracePeriodSeconds`
+  for that container into account.
+  For a failed readiness probe, the kubelet continues running the container that failed
+  checks, and also continues to run more probes; because the check failed, the kubelet
+  sets the `Ready` [condition](/docs/concepts/workloads/pods/pod-lifecycle/#pod-conditions)
+  on the Pod to `false`.
+* `terminationGracePeriodSeconds`: configure a grace period for the kubelet to wait
+  between triggering a shut down of the failed container, and then forcing the
+  container runtime to stop that container.
+  The default is to inherit the Pod-level value for `terminationGracePeriodSeconds`
+  (30 seconds if not specified), and the minimum value is 1.
+  See [probe-level `terminationGracePeriodSeconds`](#probe-level-terminationgraceperiodseconds)
+  for more detail.
 
 {{< note >}}
 Before Kubernetes 1.20, the field `timeoutSeconds` was not respected for exec probes: