Hi Sagar,
Previously I was in SAP CRM Web UI and I am new to IC Web Client. I checked the following link which describes about the configuration and rules of Intent Driven Interaction (IC WebClient) Alerts.
Configuring Interaction Center Alerts
I am still confused how to connect it with my scenario. As I described that my data (the third party system is down) will be coming through a web service. So how the alert rules can be set.