All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The narration which you mentioned in the question is reported by Al-Bukhari and Muslim but the wording is Muslim's, and it means that it is forbidden for a man to ask a woman for marriage if another brother has already approached her for the same purpose. This is in case the first man is still considering to marry her and has not yet expressed his refusal. An-Nawawi when commenting on the narration, said: 'The scholars agreed in a consensus that it is forbidden for a man to approach a woman for marriage if someone else has already approached her for marriage, and was accepted (by her guardian) and (the proposing man) did not permit others to approach her for marriage and did not give up his intention of marrying her. However, if someone else approaches her for marriage and marries her, then in this case the later has disobeyed Allaah but his marriage is correct.’
As regards offering a price for a thing for which another brother had already offered a price; he [An-Nawawi] explained the narration saying: 'Offering a price for goods for which another brother had already offered a price is forbidden when the owner of the goods agrees with a buyer to sell him the goods for a certain price but without having concluded the sale yet, then another person comes and says ''I will buy the goods from you'', this is forbidden after the price of sale has been agreed upon between the buyer and seller, whereas auction sale is not forbidden.'
With regard to applying for a job to which another person had already applied, then there is no harm in it as long as the employers did not select him for the job which he applied for, and as long as they are still studying to choose the best one among all the candidates who applied for it. Even if a given employee has been selected for a given job, there is no harm for applying to the same job especially if you see that you are more competent and capable of doing that kind of job. Nonetheless, in our view, you should not apply for this job if you think that this will cause harm to the other employee who does that job, but we cannot forbid you from doing so.
Allaah Knows best.