text: Ben, from Sheffield, was 21 months old when he disappeared on the Greek island of Kos.
  An "item" believed to have been in Ben's possession at the time was found during fresh searches.
  South Yorkshire Police said the current line of inquiry, that Ben was killed accidentally, was the most probable cause of the boy's disappearance.
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  The force said it remained committed to the investigation into Ben's disappearance and stressed the case remained open.
  Ben Needham's mother 'would tear up island' in search
  Det Insp Jon Cousins, who is leading the inquiry, said: "During the course of the inquiries we have made over the last 19 months, we have closed off a large number of theories about what happened to Ben, many of which have been open for over 20 years.
  "My team and I know that machinery, including a large digger, was used to clear an area of land on 24 July 1991, behind the farmhouse that was being renovated by the Needhams.
  "It is my professional belief that Ben Needham died as a result of an accident near to the farmhouse in Iraklis where he was last seen playing."
  The information that prompted the fresh searches was revealed to police following television appeals in May.
  A friend of a digger driver, who was clearing land with an excavator on the day the toddler went missing, said the man may have been responsible for Ben's death.
  The driver, Konstantinos Barkas, died of cancer in 2015.
  A team of 19 South Yorkshire Police officers, forensic specialists, an archaeologist and search and rescue personnel have spent 21 days digging near the farmhouse and a second site 750m away.
  Det Insp Cousins said an item, found on Saturday close to another item dated to 1991, had been shown to the Needham family.
  "It is our initial understanding that this item was in Ben's possession around the time he went missing," he said.
  "The recovery of this item, and its location, further adds to my belief that material was removed from the farmhouse on or shortly after the day that Ben disappeared."
  The Needham family, who have long believed Ben may have been abducted, have been fully informed of the force's findings.
  Speaking to the Daily Mirror before the police briefing, Ben's mother, Kerry Needham, said: "They know he's dead but just can't find him.
  "Police said it's time we ended our 25-year search. They are right but I can't say goodbye knowing he's still on that island somewhere. I feel physically sick. I can't feel any worse than I do."
  She said she just wanted to "tear up" the whole island.
  "Someone knows where he is. For God's sake, help me find him. We know he's dead but we need to find him. When someone dies you find a special place."
  Det Insp Cousins said: "Our thoughts are with the family as they are given time to digest this and they have our full and continued support.
  "Our drive has always been the family, and their welfare."
  Stephen Watson, interim Chief Constable of South Yorkshire Police, said: "To the fullest extent that we possibly can be, [we are convinced] that Ben died many years ago.
  "Our hearts go out to the family, and as a parent I can only imagine the anguish of not knowing what has happened to your youngster.
  "Every line of inquiry available to us has been pursued with the vigour that you've seen over several weeks in Kos."
target: Toddler Ben Needham "most likely" died in an accident near to where he disappeared in 1991, police have said.