Lack of evidence for an idea does not constitute evidence against that idea. However, what level of probability would you assign an idea without any evidence?

To the position I hold, that is, there is a very slim chance Jesus was a historical figure, I'll list a few ideas on backing this position; I would define slim as 10s of thousands to one.  I am not listing formal citations as this is a response to a Facebook message, not a research paper and you can easily Google anything I write.

I'll start with the writings of the Emperors Vespasian and Titus who headed the Empire from 69 to 81 CE.  They were published and discussed in detail Jewish affairs including invasions and conquests of modern day Israel, with no mention of Christ or Christianity.

Seneca the Elder and Seneca the Younger wrote in the History of Rome and On Superstition covering every cult in the Roman Empire from the first century BCE to 62 CE; again no mention of Christ or Christianity.

Claudius Charax, Aulus wrote a (lost) universal history that was a long time reference for other Authors - no quotes on the Christian Faith.

The Greek Publius Herennius Dexippus along with Gaius Asinius Quadratus both wrote histories of Judean affairs; One would think Jesus would have been important enough to mention, however, his is absent from these histories.

Collected Ancient Greek Novels (Bryan Reardon - University of California Press, 1989), and Ancient Greek Novels (Stephens and Winkler Princeton University Press 1995), the Cambridge Companion the Greek and Roman Novel (Whitmarsh Cambridge University Press 2008); all contain countless 1st century Roman satire that mocks religion, and even crucifixion, with no mention of Christ or Christianity having existed.

As a history teacher you know I could list ten pages of 1st and 2nd-century authors here, in the spirit of brevity I'll only mention one more.  Before I do, I'll admit: Lack of evidence for an idea does not constitute evidence against that idea.  However, what level of probability would you assign an idea without any evidence? 

Now there is, of course, Josephus, who decided to dedicate one paragraph (more or less) to Jesus at the end of a scroll.  Josephus was very detailed in his descriptions; that is except for Jesus.  The economy he employed in his language on Jesus is more than suspicious.  Not to mention it went unreferenced until the 3rd, or 4th century.  This paragraph mysteriously appeared hundreds of years later in the text.  Which is why it is considered a forgery.

For a new religion to start, three conditions must be met:

1) A society fragmented both racially and culturally, under the reign of a foreign power. 

2) A feudal agrarian state in which the lower class is in opposition to the official regime. 

3) A situation in which, a military solution is obviously unable to succeed in changing the political structure of a society suppressed by war or other means.  This third condition can then produce an apocalyptic, non-militarized grassroots movement. 

Anyone familiar with Christianity can link the connection of the Messianic Jews who started the Christianity to these three elements.   However, some may not know Buddhism, Islam, and the Jewish religions also come from a subject people, in relative poverty, powerless, effectively dominated by a foreign people (either directly or through collisions with an unresponsive local elite) who are racially and culturally different from themselves, and whose economic and military capability is so staggering it cannot be overcome.

Now consider the life of a Messianic Jew at the end of the 1st century.  What religious information (which can be used as power to gather and pull together an opposition group) do you have?  First you have the ancient book of Danial which reads that the Messiah should have already lived, died, and risen.   Then you have the Ascension of Isaiah written by Messianic Jews, which fulfills the prophecy in Danial, but in the Ascension of Isaiah the Messiah lived, died and was resurrected in outer space.  Then you have Paul's writings, as you know Paul didn't suggest Jesus was a physical human living just twenty years before his writings.  So how do you get your team together?  You write the book of Mark, which, in the late 1st century is the first to make Jesus a real man.  This new religion needed a human on Earth, not an "outer space Jesus" to build momentum.  Which it did, then Mathew (or Mark revision 2) followed with more details.   And then the third book - the Gospel of Luke is where all the details came to us.  All the details of the birth, life, death, and ascension of Jesus - written 100 years after the events it speaks of without a single reference to any historical data.   This is the same as if I were to write a book today about someone before WWI, to which I provide no proof, no birth record, I simply say my character was born in the second year of Woodrow Wilson's presidency.  And people buy it, they buy it to the extent that a predominant world power decided to restart the epoch to year 0 on the based on the reference date I mentioned.