But there was a tacit acknowledgement that the more time passed, the less likely it was that four-year-old Cleo would still be alive.

The unsolved disappearances of William Tyrell and Madeleine McCann, and the murder of Daniel Morcombe, were seared into most parents’ memories.

And the remoteness of the vast Blowholes campsite from which Cleo disappeared on October 16 added to the sense that police were facing a virtually insurmountable task.

So it was little surprise that even the most hardboiled detectives were reduced to tears when, against all odds, little Cleo was found – alive and well, and somehow smiling – locked in a Carnarvon home around 1am on Wednesday.

“My name is Cleo,” the little girl said when asked for her name, in an unforgettable moment captured by an officer’s body-worn camera.

WA Police Commissioner Chris Dawson broke down upon learning the news, describing it as one of the proudest days in his 45 years of service.

His deputy Col Blanch likened the investigation to looking for a needle in a haystack.

More than 100 officers were assigned to the police taskforce. Investigators worked tirelessly, processing thousands of calls to Crime Stoppers, identifying and eliminating possible suspects and searching places of interest.

Sophisticated technological assistance from the Australian Federal Police was gratefully accepted.

Surveillance footage from motels and children’s clothing stores within a 1000km radius of the campsite was sought and forensic officers sifted through more than 50 cubic metres of rubbish, from roadside bins stretching from Minilya to Geraldton.

The state government also swung into action, offering a $1 million reward for information leading to Cleo’s whereabouts – an unusual step at such an early point in the investigation.

No stone was left unturned.

“I haven’t slept, the commissioner hasn’t slept. I don’t think anyone in this police force has slept,” Mr Blanch told Perth radio 6PR.

“We have held on to this hope from day one and for it to come real today, it’s just an outpouring of relief.”

A 36-year-old man from Carnarvon was in custody on Wednesday and was being questioned in relation to the suspected abduction.

Police say he has no connection to Cleo’s family and was not present at the house when Cleo was found.

Authorities have so far been tight-lipped on the exact intelligence that led officers to the property just minutes from Cleo’s family home.

“There were lots of things. There were car movements, there were phone movements, there were antecedents of people,” Mr Blanch said.

“The jigsaw fit but it took really good intelligence analysts, detectives and specialists to look at all of that information, put it together and say ‘that doesn’t look right to me’.”

University of Newcastle criminologist Xanthe Mallett said WA detectives had learnt from other child abduction cases, describing Cleo’s discovery as a “once-in-a-lifetime miracle”.

“The feel was that Cleo would be the next William Tyrrell and next Madeleine McCann. We would never find out what happened,” she told Nine’s Today program.

The parents of Daniel Morcombe, who suffered the horror of their 13-year-old son’s 2003 abduction and murder, also paid tribute to WA investigators.

“Excellent detective work by Western Australian Police and a vigilant community,” Denise Morcombe posted on Twitter.

NSW Police Commissioner Mick Fuller said it was an amazing result and a tribute to the WA officers’ leadership and determination.