Is Bitcoin mining chance based? This answer says that Bitcoin is not chance based, may I know how it is deterministic and does not have any associated probability of mining a coin?
To sum up the mining process: miners have a potential future block and they need to solve a problem based on that block to prove that they worked on it (Proof of Work). They apply a hash function to the block and get back a hash. The hash needs to have some properties, e.g. start with 3 zeros. If it doesn't, the miners change a value in the block (called nonce) and apply the hash function again. The new hash will be different. If it still doesn't start with 3 zeros miners repeat the process until they find a hash that starts with 3 zeros. For more details, please read this to understand the mining process.

A hash function is in itself deterministic. However, the mining process is not. Thus, the answer in the link you provided is wrong. If everyone was trying to mine identical blocks with identical nonces of the same exact order then it might be, in a sense, deterministic but that is not the case. 

Everyone has a chance to win (although it is so small that in practice doesn't occur). See here for some examples.