Is it in reality one single long table spanning several pages? If you select the entire table (using the right click context menu, or clicking the top left corner where the mouse points down to the right) does it select "all" of your tables?
It sounds like the tables are in linked frames, and the overflow from the first table appears on the second page, the third table is an overflow from page two. The second and third tables are actually a continuation of the first one.
If that is the case, that is as it should work in InDesign.
If you start a new table with Table > Insert Table, that should work independently of the first table.
Jongware - when I select through the context menu by following your instructions, it selects all the tables on the pages. I didn't create the document myself, so I am not sure how the tables got inserted.
Steve - the page overflow doesn't wrap to the next page, so maybe it's not using linked frames.
I wanted to add that each table is in its own object (delimited by a red box).
If choosing Select All selects the content of all the tables, then they are all part of the same table.
If you want to separate them, then you need to select the table rows you want to separate, cut them, and paste them into a new table.
It sounds like you may be new to InDesign. I strongly suggest that you get a beginner's book. An excellent one is Sandee Cohen's InDesign Visual QuickStart. There are versions for different versions of InDesign.