Many of the big landowners in Ireland in the 1800s had borrowed heavily against their estates. They relied on the rental income to service their loans. During the mid 1880s, the famine and other factors meant that many tenants either could not pay their rents or could not pay in full (and many also died or emigrated which reduced the rental income too). The consequence was that many of the owners ended up in serious financial difficulties and faced bankruptcy. The extent of this was so widespread that some of the banks who lent the money also faced potential bankruptcy. (Somewhat similar to recent financial crises around the world where lenders lent rashly against assets that proved to be overvalued). The solution in the 1850s was the creation of a special process and eventually a court for enabling them to sell their estates at a fair market price (which would go to the lender) but after which any outstanding debt would be written off.
As with any sale process, an inventory was drawn up showing what the property consisted of, including any sitting tenants. The potential rental income, and existing tenure, was clearly a critical piece of information for any prospective purchaser. So probably Laurence Leary was a tenant on an estate that was being sold under Estate Courts process, possibly in 1854. The inventory normally would detail all the properties for sale, by townland, (similar to Griffiths) together with details of the leases ie when granted, and when it would expire etc. Sometimes people had 3 lives leases and this can be very useful in genealogical terms as it would list the 3 lives and their relationships, so you might get several generations named. Not always though.
I can’t help you with the 1866 date but the mention of probate would suggest that someone had died and that there was a winding up of an estate, but as Shane has said, you would need to get the documents to get the whole story.