Constables Matthew Arnold, 26, and Rachel McCrow, 29, along with 58-year-old resident Alan Dare were gunned down in Wieambilla, in the western Darling Downs region, on Monday evening.

Their killers – former school principal Nathaniel Train, his brother Gareth and sister-in-law Stacey – died in a firefight with heavily armed tactical officers later that night.

Another two constables who were called to the property – 28-year-olds Keeley Brough and Randall Kirk – managed to escape.

Queensland Police Commissioner Katarina Carroll said investigators would look at the killers’ possible extremist links after a series of posts under the name of Gareth Train were uncovered on conspiracy theory forums.

The posts include references to anti-vaccine sentiments and claims high-profile shootings were hoaxes or false-flag operations.

“It’s very difficult at the moment for us to reason with what has happened, there are no obvious reasons,” Carroll told ABC’s 7.30 program on Tuesday night.

“But within the next few days and the next few weeks, I have no doubt that we will come back … (with) some insight into what we believe took place.”

Carroll said every possible motivation for the killings was being looked at, including whether it was a premeditated attack on the officers.

“Some of the stuff that’s online from these people, we will investigate what they have been doing not only in recent weeks but in recent years, who they’ve been interacting with … their online presence, every aspect of this will be thorough,” she said.

The police commissioner described the deadly shooting as “senseless and callous”.

Prime Minister Anthony Albanese echoed her sentiments as he paid tribute to the slain constables and Dare.

“This is not a price that anyone who puts on the uniform should ever pay. We can never count the true cost,” he said on Tuesday.

“My heart goes out to the families and loved ones of all those affected by this tragedy. With honour they served, and Australia mourns with you.”

-AAP