Noob question about finite bitcoin amount, mining, and updating the ledger

Once we reach the limit of bitcoins to be created, what will encourage miners to continue updating the ledger? - Does this question make sense?

As far as I understand, the motivation today is the bitcoin reward, so it pays off to have a mining operation since the value of the rewarded bitcoins is greater than the costs of running such operation. What will happen when that rewarded amount becomes less than the cost of running the operation (i.e. electricity costs etc).

This question has probably been asked before so I appreciate the patience.