Here's one possible response:
Both these sources are real news sources according to Wikipedia. The alligator story is real. If I had to pick one of the two I would pick the first TV station (abcnews4) in this case because they are more local to the event (they are in Charleston, the city where it happened) vs. the KDVR story which seems to just be reprinting someone else's story (and is in Denver, not South Carolina!)
How do we get there? We start by doing our "just add wikipedia" trick. Let's show the ABC one first:
We search the URL or domain and add our bare keyword "wikipedia". Selecting the most relevant search result we find it is about a local TV station in Charleston. Just to be sure the article is for the right site, we scroll down and make sure the URL matches. It does!
What about KDVR?
We do the same search for the URL or domain adding our bare keyword "wikipedia". When we get to the article we find it is a local news station in Denver — very far away from the event. It is a real news station (the URL checks out) but it is really just re-reporting what others have reported.
Here's our first reflection: we often talk about authority being "contextual and constructed." Let's take that "contextual" piece. An organization that might have authority in one area, but won't have the same level of authority in all areas. For example, a fitness instructor might be a great person for advice on a fitness routine, but you wouldn't get medical advice from them. Likewise, you might ask your doctor about an illness or medical condition, but you wouldn't expect them to be an expert in aerobics.
Local and national newspapers employ reporters that have very similar skills, much more similar than fitness instructors and doctors. But even here authority differs depending on the type of story. For your first reflection, think of a sort of story where a local paper would have a high degree of authority. Then think of another sort of story where they might have far less authority.