Given a blockchain using Proof of Work, where the hash function produces a $256-$bit output and the difficulty D$=220,$ calculate the target hash T using T$=2^256/$D $.$ Explain what the target hash represents in the mining process.

If the difficulty increases to D$=224,$ compute the new target hash. Calculate the probability of finding a valid hash in one attempt for both difficulty levels and explain how increasing D impacts mining difficulty.