How miners with less power win? As I understand, when multiple persons mine blocks, only the first one who  solves block is the winner and gets rewarded.

Basically the winner is the one (solo miner or group in pool) who has the most computing power.
That said, when the next block is being mined, again the same person will win because of his computing power. 

My question is, how the other mines with less power get chance to win i.e to find the hash of the block before the most powerful miner (regardless if that is person or group) ?
That said, when the next block is being mined, again the same person will win because of his computing power.


No. Higher mining power means just higher chances to mine a block.

If there are 3 miners:


Miner A with 4 Gigahashes per second
Miner B with 6 Gigahashes per second
Miner C with 1 Gigahash per second


Together, they can hash 11.000.000.000 times per second (4+6+1 gigahashes).
The probability for the first miner to win is 4/11 = 36%, the probability for the second miner to win is 6/11 = 55%, the probability for the third miner to win is 1/11 = 9%.

If miner B hashes the block, the next block can of course also be hashed by miner A, B or C.