Probation in criminal law is a period of supervision over an offender, ordered by a court instead of serving time in prison. In some jurisdictions, the term probation only applies to community sentences (alternatives to incarceration), such as suspended sentences.
When your landlord changes your door locks because you are behind on paying the rent, the landlord must give you advanced written notice of the proposed lock change AND a written notice at the time your locks are changed.
As a rent-stabilized or rent-controlled tenant, you may request that your landlord replace a broken appliance with a new one, and in doing so, you consent to a monthly increase in your rent. You can do this in a letter or a phone call. Many landlords are happy to do this if they can get the increase.