Short answer--because he has jursidiction.
And you can't exactly say the marriage was invalid from the start either.
Law is a little complicated. You might have a marriage for some purposes but not for others; a marriage, illegal when contracted, might nevertheless be valid for purposes of making the children legitimate; for conveying to the wife marital property rights; or for making property community property; or for putting the wife in a position from which she could not contract the next marriage without committing bigamy. Depends on local law.
But, you can say with some confidence that a judge who has jurisdiction over the parties can affect whatever marital rights exist and title to whatever property is subject to marital rights and the custody of minor children who result from the relationship and their support as he determines to be appropriate.
A few pages of posts before yours is a post describing the quirks of the Coast Provines's becoming part of the Republic of Kenya. IIRC, the courts there were not the standard English derived affairs, but were islamic in nature.
Views were divided as to whether the coastal strip should be treated as a single entity with Kenya Colony, or whether it should be handed back to the Sultan of Zanzibar or it be treated as an independent entity and declared Independent.
In a report submitted to the British Government and the Sultan of Zanzibar entitled ‘The Kenya Coastal Strip Ð Report by the Commissioner’ Mr. Robertson recommended that the coastal strip be incorporated into Kenya before self government and independence subject to certain safeguards being given to the coastal people which should be entrenched in the constitution.
... Robertson further recommended that the British Government abrogate the 1895 Agreement with the Sultan of Zanzibar and that another Agreement be made between the Government of Kenya and the Sultan of Zanzibar whereby the Sultan of Zanzibar will surrender his Sovereignty claims over the Coastal strip in consideration of the Kenya Government undertaking to respect and safeguarding inter alia the maintenance of the Sharia Law for Muslims and the retention of the Kadhi’s Courts...
On the 5th October 1963, the said Agreement was actually executed in the form of an exchange of letters between the Prime Ministers of Kenya and Zanzibar Messrs Jomo Kenyatta and M. Shamte respectively.