Let's 1st understand what these planets represent on their own?

Sun - Sun represents Soul, Personality, King, Government, Father, Authority, Career, Top Positions, Ego, Self Esteem, Health, Education etc.

Mercury - Mercury represents communication skills, marketing, calculative ability, younger siblings, hobbies, skills with hands, intelligence, quick decision making, logical thinking, youthfulness etc.

Saturn - It is all that which we don't like in our life. Saturn is Delay, Frustration, Restriction, Limitation and Anxiety. It is people of Authority, like Boss at your Work Place or Father-Figure at Home. Saturn is our Karmic Debt from past-life. Saturn is the things we didn't treat too well in our past life. Saturn is our Challenges and Lessons of life. Saturn is Old-Age, Teeth/Bones in Human Body, Diseases, Changes etc. Saturn represents our Step-Relations, it means that wherever Saturn sits, people related with that house give us Step Treatment. Saturn is Hard Work, Efforts and most importantly Perseverance etc. Nothing comes easy and in one go with Saturn. You have to work hard continuously over the longest possible period of life. Saturn makes a person Legend as Legends have one thing in common that they choose one field and work hard in it for whole life. 

3 planetary conjunction - Whenever 3 or more planets are conjunct with each other in a house/sign then things related to that house/sign become a kind of life focus for person. It is because of huge accumulation of energy within 30 degrees of sky. It means not only these 3 planets' energy is going into this house/sign but the energy of at least 4 to 6 house/sign is going into this house/sign as these planets will be ruling some houses too. So, this house/sign with conjunction becomes almost the most important house in chart. During Career Consultation, I give a huge importance to any such house which has 3 or more planets in it.

House Ruler - Besides these karaka things, Sun, Mercury & Saturn will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include things related to the houses at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas.

Meaning of Sun-Mercury-Saturn Conjunction - This conjunction can create serious troubles in person's ability to communicate with others as Mercury is with 2 strong malefic planets. This impact can be seen more severely in early age. Person may start speaking late or may have troubles in speaking. As Mercury represents nervous system, this also makes a case where person can have serious problems in understanding or comprehending things. Even if person doesn't go through these troubles, he can still be talking very less and only when it is most necessary. This scenario can be more visible if Mercury is between Sun and Saturn degree-wise which will create a Paap Kartari Yoga for gentle Mercury. At the same time, this person can be very good in Legal Communications. His drafting skills can be very good. As Sun & Saturn both are related to Law & Governance, they can become Lawyer or Activists. If anyone thinks that Lawyer is a profession of speaking a lot then it is not the case. A good Lawyer is one who covers the whole case in minimum precise words. So, this conjunction can actually help being a Lawyer as person will be very precise and specific about his words. This conjunction can create troubles with siblings. This is also a situation where relation with Father can go for toss due to Sun-Saturn coming together. Things related to the house where this conjunction falls will prosper only in 30s of person. Till then it is all hard work. Their career and authority will come after delay and hard work. When they communicate, they only communicate about what is real. They will never gossip or they will never have an unreal communication. 

Who will win the Conjunction? - Saturn is there, so it's all Saturn's game. 

Dignity & Strength - 

As Saturn is involved, in any house/sign results will be more or less same and person will have to put his best work to get any good result out of Saturn.