Update Row Value If Another Row is Deleted

Hello.

The app I am building has a ranking system. Nothing fancy, just 1st, 2nd, 3rd. Is there any possible way using CodeIgniter, I could update values in the other rows based on the row that is deleted?

So, If for example,  I delete 1st place from the table, 2nd would become 1st and 3rd would become 2nd.

I have started trying to build a formula in PHP using the rows Rank Value and the number of rows in the table, but it is proving quite challenging and I was just wondering if there is a simpler way using a CodeIgniter feature.  I did try a Google search but I could not see any results that mention anything.

Thank you for any help.