This expression will hopefully give you what you need (a number from 1 to 3 depending on what third of all rows the particular row belongs to, you can use that number to create the text field value as you want it):
ceil(rowno(total) / (ceil(noofrows(total)/3)))
The second part of this expression - ceil(noofrows(total)/3) - calculates how many rows that should go into each third, and by dividing each row number with that number we can find out the correct third.
Be aware that if the total number of rows are not evenly divided by 3, the last third will contain fewer rows than the other. If for example you have 10 rows, there will be four rows in 1st Third and 2nd Third, but only two rows in the 3rd Third.
Naturally, the "thirds classification" is not tied to each individual row's data, so if you sort the table differently the rows currently on top will still be 1st Third.
