You may have noticed that some artifacts are more difficult to find than others.
Rarities for artifacts are set by collection (or sets). This means that your are more likely to find items from a given collection than another. For example, the Junk collection is more common that the Royal collection.
Within a given collection all items are equally as likely to appear. This means that you are equally likely to find the Old Dentures than the Old Boot. However, randomness being what is, you will sometimes find that you have a lot of a given artifact and few of another. This is normal.
Whenever you are struggling to find a certain artifacts, trading with friends is a fun and effective way to find them.
Happy treasure hunting!