You are only liable to pay CGT when you sell the property. If you haven't sold it, no CGT (yet). End of.
The amount of CGT liability, when it occurs, will be assessed on the difference between what you eventually sell at, minus the probate value, minus the allowable cost of capital improvements, as debated by others above. So keep records and receipts, as you may need them later.
Finally, in the tax year in which you sell (realise the value of the asset), you will be able to deduct your annual exempt amount, as covered by NJ above.