For example, if a mining pool own 20% of the total computation power, they have 20% chance to solve the proof of work problem faster than others and win the block reward.
The word "faster" is probably misleading and wrong to use, it doesn't matter how fast you are, blocks are found once every 10 minutes on average regardless. also, keep in mind that miners are not working on the same block, and there is no such thing as "the next block", every miner is working on a different unique block candidate, a pool that has 20% of the hashrate is very likely to find 20% of the blocks at no exact order, speed or pace.
Can there be a back-to-back winner or do winners for the POW challenge get excluded from the next challenge round? 
There is no "next challenge round", as explained above, miners create their own blocks, and to keep this "chain" theory intact, they all have the previous block hash in common when a miner manages to construct a valid block, they inform the rest of the network and everybody continue to do exactly they were doing with the expectation of using the "new block hash" and deleting the transactions that have been already included.