There is no such thing as probate in Scots law.
When someone dies domiciled in Scotland, the estate is dealt with in the Scottish courts, by the process of Confirmation. All Confirmations to 1925 are listed on the Scotland's People web site under 'Legal Records'.
If, and only if, the person owned property in England or Wales, the Scottish Confirmation is then Sealed in an English or Welsh court. Sealings of estates in the English/Welsh courts are listed along with Probates on the official government web site
https://probatesearch.service.gov.uk/#wills. These are organised by the date of probate/sealing, not by the date of death, so it's always wise to search the year of death and a few later years. (I usually search for five years but some do take even longer than that if there are complications.)
FindMyPast has an index to the English/Welsh Calendar of Probate, which includes Sealings of estates Confimed in Scotland. (This is not, however, accessed via the 'Wills and Probate' tab as you would expect, but via the 'Civil Deaths and Burials' tab.)
I have searched all three of the above (using Macintosh, Mackintosh, McIntosh and McKintosh), and, as
GR2 says, there is no listing of a Margaret MacIntosh who died on 5 December 1912.
A Miss* Margaret Mackintosh, aged 74, died in Edinburgh St Andrew in 1912, but her death registration was No 8, which means she must have died very early in January, or possibly on one of the last few days of December 1911 (it was at that time obligatory to register a death within eight days). There are three more deaths of Margaret M*c*n*t*s*h in Edinburgh in 1912, but all three were married women.
*I am assuming that your Margaret Mackintosh was 'Miss' because in Scotland a married woman is listed by both her maiden and her married surname, and the England/Wales Calendar of Probate lists both surnames of married women whose Scottish Confirmation was Sealed in England/Wales.