(a) A caveat against the allowance of an instrument as a will shall be received by the Court of Chancery at any time prior to the entry of an order of probate. The caveat having been received, the Court shall appoint a time for hearing and award citations for the parties interested, and order service or publication of notice to the parties not within the State in accordance with § 1303 of this title. If, when a caveat is received, a time be appointed and process issued, it shall not be necessary to adjourn the taking of the proof and hearing; but an adjournment may be decreed, and other process awarded, or order made.
(b) The Court of Chancery may determine the costs occasioned by such caveat and decree the payment thereof.