I could imagine some behaviour along those lines in search engines, specifically if you're searching for similar documents. Which none of them seem to — would be useful! Let me know if I'm wrong! — but imagine a search engine that lets you look for documents 'similar to this document here'. Also imagine that's threshold-based; you want equal levels of similarity regardless of the rarity of the input document.

In that case, as the size of the corpus grows it should get easier to find ones in the right range of similarity.