The sibling comment is exactly right. Your odds of mining a specific block are altered, but this doesn't mean much. If everyone else but you disappeared from the network, without a difficulty retarget, your odds of mining the next specific block are 100%. The rate at which you mine these blocks is exactly the same as the rate at which you mine blocks when you represent 1% or 0.1% of the network hashrate.
Example: Fixed difficulty, so 1/1,000,000 hash wins, 1,000 hashes/sec.
a) You are 100% of the network hashrate. Your odds of finding the next block are 100%. After 500 seconds of mining, your odds of having mined 1 block are 50%. After 500 seconds, the network will have produced on average 0.5 blocks (I know, awkward.)
b) You are 1% of the network hashrate. Your odds of finding the next block are 1%. After 500 seconds of mining, your odds of having mined 1 block are 50%. After 500 seconds, the network will have produced on average 50 blocks.