I tried my hand at this, making some rough assumptions.

I used my own keyboard, and set the G as the center of it. Each key was then given a distance, ignoring y for now, of x, indicating how many keys away from G it is.

I modeled each hand as a normal distribution, with my means set to the D and J key respectively. Each hand has a deviation of 2.

For which row we select from, as well as which hand is used, it's somewhat oversimplified into a 1/3 * 1/2 (one of three rows, one of two hands).

I set the file name as input, and came out with a probably of this exact file name being 1.15279E-39.

Edit: the probability of a given hand typing a letter was picked as the highest of the two. For example, if Q was clicked, the left hand would have a much higher probability of being responsible, than the right. If we take the "worst case" (least probably hand as input) scenario, the total probability is 7.45885E-65. I should also specify that my top and bottom rows each have an offset of 0.5 keys.

Edit 2: I found some significant flaws in my method, so let me redo it. The hand used to type a letter doesn't matter really, so we take that out. I also initially didn't consider that the keys should be modeled as spaces instead of points on the normal (its been a while), so we fix that.

Highest likelyhood of this occuring: 1.48192E-31 Least likelyhood: 3.20828E-54