This might not have any major impact on the SEO, but basically I have a random blog at this URL: http://example.com/blog (not a real URL), that I am removing and replacing with a company blog.
I want to use the http://example.com/blog URL address, but I'm not sure how this would affect my SEO since this random blog content that I am removing has the example.com/blog URL prefix.
Should I add a 301 redirect for those old blog articles and leave the basic /blog URL without any redirects?
You're going to use your same host + folder for publishing a totally different blog, right? then there are many alternatives:
If you are going to publish your old posts using new URL's and want to keep their pagerank then you must configure 301 redirects: Something like: example.com/blog/your-old-url redirect(ing) 301 to example.com/blog/your-new-url.
If you want to keep your old pages just like they are right now you don't need to do anything about it, let them live just like they are at their current URL. So if you have example.com/blog/your-old-url, just leave it like that or add it like that if you have new CMS.
If you don't bother about your old posts then forget about them, you don't need to do anything.
If you will move all your old random posts to a new folder and you want to keep their pagerank, then you have to configure 301 redirects from the old url to the new one.
301 redirects are intended to tell crawlers your website's address or page's urls has changed, and you want to tell them your old url has gone forever while giving them the new location.
What you can do is just redirect your old page URL to your targeted URL. When you have done this when user click old URL then that page redirect to your new page URL.
