The Romans murdered John the Baptist as The Christ. The Flavians hired Josephus to cover it up.

Josephus was born in Jerusalem in 37 AD, supposedly (by Josephus' account) to a father "of priestly descent" and a mother "whom claimed royal ancestry". According to Josephus. Josephus was appointed military commander of Galilee by Judaeans revolting against Rome, and he supposedly fortified the towns of the north before eventually surrendering to Roman forces... after which time he betrayed his family and friends and joined the Romans at the siege of Jerusalem in 70 AD. Of course, giving himself these pseudo noble-spiritual entitlements was easy to do since his writings took place many years after the fall of Jerusalem and the diaspora, when the outcomes were already known, when most if not all of the witnesses against him would heave been deceased, and his writings were most-likely hyperbole tacitly condoned by the Flavians in order to attempt to lead latter Judeans into believing that the Judean nobility and priesthood were backing the Romanization of Judea. After the fall of Jerusalem, Josephus  moved to Rome and became a writer (historical propagandist) for the Flavians. As a subject of the Flavians, he obviously had to write his accounts with a pro Flavian-centrist mindset, making his accounts suspicious at best.

As Wikipedia states: "...The Flavians also controlled public opinion through literature. Vespasian approved histories written under his reign, assuring biases against him were removed, while also giving financial rewards to contemporary writers. The ancient historians that lived through the period such as Tacitus, Suetonius, Josephus and Pliny the Elder speak suspiciously well of Vespasian while condemning the emperors that came before him. Tacitus admits that his status was elevated by Vespasian, Josephus identifies Vespasian as a patron and savior, and Pliny dedicated his Natural History to Vespasian's son, Titus. Those that spoke against Vespasian were punished. A number of Stoic philosophers were accused of corrupting students with inappropriate teachings and were expelled from Rome. Helvidius Priscus, a pro-Republic philosopher, was executed for his teachings."

When the Romans found out that John had attempted to reinstate his father as the High Priest, they had him murdered.

The youngest Flavian - and the last to reign (81-96 AD) - Domitian - upon ascending the throne as emperor, went about pseudo-deifying his father and brother as well as other family members. Again, from Wikipedia: "Domitian's first act as Emperor was the deification of his brother Titus. Upon their deaths, his infant son, and niece Julia Flavia, were likewise enrolled among the gods. To foster the worship of the imperial family, Domitian erected a dynastic mausoleum on the site of Vespasian's former house on the Quirinal, and completed the Temple of Vespasian and Titus, a shrine dedicated to the worship of his deified father and brother. To memorialize the military triumphs of the Flavian family, he ordered the construction of the Templum Divorum and the Templum Fortuna Redux, and completed the Arch of Titus. In order to further justify the divine nature of Flavian rule, Domitian also emphasized connections with the chief deity Jupiter, most significantly through the restoration of the Temple of Jupiter on the Capitoline Hill." For context, the Roman paternal deity Jupiter assimilates both to the Greek paternal deity Zeus as well as the Egyptian paternal deity Ptah. 

Although Josephus had been in the care of the Flavians since around 66 AD, it wasn't until the waning years of Domitian's reign that Josephus wrote his "histories", which chronologically coincided with the time frame of Domitian's paranoid lust for deifying his family. The Gospel of Mark dates from c. AD 66–70, Matthew and Luke around AD 85–90, and John AD 90–110, meaning that three of the four gospels were "coincidentally" written during the same period that Josephus was in the hire of Domitian - perhaps being sourced from the earlier gospel of Mark whose true author may very well have been Josephus as well. Simply put, Domitian was a spiritually paranoid sociopath whom had at his disposal the amoral and unethical literary lackey Josephus, whose writings "coincided" with the writing of three of the four gospels, which were most likely all based upon the earlier gospel of Mark, which was written around the same time that Josephus was first taken in by the Flavians.