What is the probability of generating 6 sequential blocks, less than an hour?
I would first like to comment that there is widespread confusion about how double-spending works. In particular, the question you've asked here is irrelevant. I urge anyone who is seriously examining this issue to carefully read Analysis of Hashrate-based Double Spending, which also examines the effect of changing the average time between blocks.

For your question as is - do you mean


The probability that in a given hour, the miner will find at least 6 blocks? Or
The probability that the event "the miner finds 6 blocks in a row, without the other miners finding blocks between him" will happen in a given hour?
Or something else?


The first option is relatively easy - If the average time between blocks is T, the miner's proportion of the hashrate is q, and you're looking at a time period S, he will find on average (Sp/T) blocks, following the Poisson Distribution. So the probability this will be at least 6 is

1 - \sum_{x=0}^{5} (exp(-Sq/T) * (Sq/T)^x / x!)

For example, if q = 0.5 then that's 8.4% for 1 hour, and for 1 day it's 99.9999999999999999999999%.

I'll need to work out the 2nd option, but the answer to the easier question "What is the chance to find 6 blocks in a row starting right now" is of course q6.