Hikmat al-Rawashdeh, a lawyer for the defendants, said that the case was politically motivated and designed to undermine support for Hamas after an outpouring of support from ordinary Jordanians following Israel's 22-day offensive in the Gaza Strip.
"It's not a crime to take pictures of public locations that are available even on the internet on Google," he said.
At the opening of the trial last year, the military prosecutor said that Hamas had provided the men with military training in an unnamed neighbouring country.
The military judge at the state security court initially sentenced the three men to 10 years, but then halved the sentence.
Two other men were acquitted at Wednesday's trial for lack of evidence.
Last year, a group of suspected Hamas fighters were convicted of preparing attacks inside the kingdom.
Jordan outlawed Hamas - which seized full control of the Gaza Strip in June 2007 after pushing out security forces loyal to Mahmoud Abbas, the Palestinian president - in 1999.
The Amman offices of the Palestinian movement were closed and senior leaders were expelled.