Now I get, that’s why both the transactions, the first one and second one both have almost same chance of been confirmed, since the node that holds the first transaction could still add it to the block it mines (if the fee later meets the node’s requirement), if he mines first before the other block and then it invalidates the second transaction
Nodes do not necessarily mine bitcoin but miners pick transactions from nodes' mempools. Miners will most likely pick the transaction paying higher fee rate and ignore the other one.
The chances of getting included into a block depends mostly on the level of propagation of each transaction, though.