In New York, the probate process involves validating a will in the Surrogate's Court, ensuring its legality and authenticity. If there is no valid will, the estate goes through administration. While probate involves distributing assets as outlined in the will, the administration typically follows the state's intestacy laws, guiding asset distribution for those who pass away without a will. It's essential to consult an attorney familiar with New York estate law to navigate these processes effectively.