What are the odds of discovering a block as a solo miner?
Take the total network Th/s and divide by your total Th/s. That number gives you you a number that tells you how many blocks will occur before you get one (on average).

So if there is currently 3,666 Th/s on the network, and you have a 0.55 Th/s (like you would if you have a $5,000 KNCMiner Jupiter ASIC), then 3,666/0.55 = 6,665.

That means you have 1/6,665ths of total hashing capacity.   There will be 6,665 blocks before you get one.

So if there are 144 blocks in a day, then you need to wait 46.28 days to get a block when mining solowith that hardware.  But that is assuming difficulty doesn't rise.   So what will happen with a rising difficulty is you end up waiting much longer even, and possibly never end up getting a block when solo mining.

That's why solo mining is not as profitable as using a pool for anyone without tens of Th/s nowadays.