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.

Ketu - Just like Rahu, Ketu also represents Illusion as both are ilusionary planets but the difference is that Ketu is also the one who removes the illusion and brings enlightenment. Besides this, Ketu represents Isolation, Separation, Spirituality, Mystical World, Other Dimension means things related to Alien World, also represents Son, Dog, Intuition, Research Ability, Curious Nature, things which we have already achieved in past life and not much concerned to perform in this 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 & Ketu 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-Ketu Conjunction - This is another conjunction where person is born near solar eclipse. Closer Sun and Ketu are degree-wise, the more impact you will see of Sun being eclipsed which indicates towards loss of father, ego or confidence in early life. Person can have loss of self/identity in early life at least. At the same time, person can be of very inquisitive nature as Ketu represents research & investigation and Mercury represents Collection of information. Here, negative impact will be on person's communication ability or relation with Authority/Father/Sibling. If Mercury is in between degrees of Sun & Ketu then these results will be more evident. Positively, person will be very much interested in communication of secret and hidden matters. He can have very secretive ways of communicating or his whole personality can be a secretive one. It means that he may not be very expressive in normal routine of life but expressive only in specific situations. If Ketu and Mercury are too close degree-wise then it creates a situation where person can have problem in grasping or comprehending things in early life. At times,it can cause issues related with nervous system. 

Who will win the Conjunction? - Ketu is impacting both the planets. So, Ketu rules over the conjunction. 

Dignity & Strength - 

In any sign/dignity, Ketu will play its role of isolation/separation from karakas of Sun & Mercury. It is only in Aries or Leo, Sun gets some strength to withstand the eclipsing effects of Ketu, else it is all Ketu game till middle age.