Application Insights and kubernetes: How to not log successful /liveness and /hc probes to trace logs

In your configuration of the liveness and readiness probe you can specify custom headers to send along with the request, for example

          livenessProbe:
            httpGet:
              path: /api/health
              port: http
              httpHeaders:
              - name: HealthProbe-Type
                value: Liveness
          readinessProbe:
            httpGet:
              path: /api/health
              port: http
              httpHeaders:
              - name: HealthProbe-Type
                value: Readiness 

You can then filter based on that header in your implementation of ITelemetryProcessor:

public class HealthProbeTelemetryProcessor : ITelemetryProcessor
    {
        private readonly IHttpContextAccessor _httpContextAccessor;
        private readonly ITelemetryProcessor _nextProcessor;
        public static string HealthProbeHeaderName => "HealthProbe-Type";

        public HealthProbeTelemetryProcessor(IHttpContextAccessor httpContextAccessor, ITelemetryProcessor nextProcessor)
        {
            _httpContextAccessor = httpContextAccessor;
            _nextProcessor = nextProcessor;
        }

        public void Process(ITelemetry item)
        {
            if (item == null) throw new ArgumentNullException(nameof(item));

            if (!string.IsNullOrWhiteSpace(item.Context.Operation.SyntheticSource))
                return;

            var isNotRequestTelemetry = !(item is RequestTelemetry);
            
            if ((isNotRequestTelemetry || _httpContextAccessor.HttpContext == null || !(_httpContextAccessor.HttpContext.Request?.Headers.ContainsKey(HealthProbeHeaderName)).GetValueOrDefault()))
                _nextProcessor.Process(item);
        }
    }