The first thing to do is look at the overall objective of how powerful you want the character to be in combat. Worry about their skill later.
The noble would likely be a level 1 character at most, so where can he get higher level skills from?
The blacksmith may have some experience, due to a lot of training with the gear he uses to ensure it stands up to what it needs to, but he doesn't need to be high level... Maybe 1/4 of the party (as a very rough example).
5e gives us a couple of prime examples on how to ensure this works; Bounded Accuracy, Proficiency, Expertise, and Advantage.
Because of bounded accuracy, it is highly likely that the noble can be more skilled than an unskilled adventurer merely based on stats and 'trained skills'. This means that an NPC (0/1-level) with Persuasion trained and a 16 charisma will have a higher modifier than a 5th level adventurer with a 12 charisma.
As their training is focused, they are likely to have more proficient skills/tools than a player character that are specifically isolated to their area of training, and a simple tool built in to the downtime rules that helps to explain extra areas of training for NPC's outside the character stats.
Granted, the downtime rules cover 'tools,' and not 'skills', but it is not too difficult to state that a non-adventurer can be focused enough to learn new 'skill' proficiencies in this method.
Although given to only classes like Rogue and Bard, expertise is extremely appropriate for a non-adventurer that tries to focus on specific skills.
Since an NPC is not as broadly trained and skilled as a Player Character (generally speaking), they can have the focus of a rogue or bard if necessary to allow their skills to shine as they should.
Expertise for a level 1 character/npc would be a +4 to the skill, thus keeping them on par with most proficient level 10-14 adventurers with similar stats. This is a great balancing factor in low level npc's that deal with high-level PC's, and still gives a great reason that the King doesn't fight his own fights (hiring adventurers instead).
This is easy to give an NPC that little bonus that pushes them over the top. Perhaps they have better quality tools and facilities, perhaps they are working with specific resources that they have specifically trained in. Anything like this can give an already skilled NPC the home-court advantage, and thus give them advantage on the roll.
Advantage means a lot. This is especially true when NPC has slightly lower skill than the PC's.
The foppish noble has been working on the policies in the kingdom for quite a while and has the current policies set up specifically to favor him. He has advantage on checks associated with political matters in the kingdom.
The blacksmith has a dwarven-built forge and adamantine tools. The high-quality allows his work to reach a whole new level, giving him advantage on all checks associated with his forge/tools.
By understanding the bounded accuracy system, and using the tools that are already built in to the system, it is reasonable and relatively simple to give low level NPC's the ability to compete in skill with characters of much higher level. This adds a nice level of realism for those that may want it in their game.
Ultimately, it is up to the DM to figure out how to determine the levels of NPC's and their relationship to the player characters. Do what works for your game.
It is also possible to consider an NPC as a 'leveled' character that simply doesn't gain hit points, and doesn't have many/any weapon/armor proficiencies (thus still having a higher proficiency modifier), but the above methods are likely to work without having to doctor the system much.