Why Collector-to-Base currents ratio in a BJT transistor is always greater than 1?
Your Q apparently refers to a NPN transistor ('holes injected into Emitter').

In a bipolar transistor (NPN or PNP; referring to NPN in this answer), when the base-emitter junction is forward biased, current flows. This consists of holes injected from the base to the emitter, and electrons from the emitter to the base. Transistors are constructed (richer doping of Emitter than Base) so that most of the current is carried by electrons rather than by holes.

Now, the holes injected into the emitter will find a dense field of electrons (emitter is heavily doped), and so will recombine quickly. This requires replacement electrons to be supplied by the emitter terminal.

Electrons injected by the emitter into the base will find very few holes around -- the base is relatively lightly doped. So, a relatively small amount of recombination occurs, although this does require holes and consequent base current. As soon as these electrons arrive at the base end of the depletion region, they diffuse away from it. because the base is thin, this diffusion is 'fast'. 

Any electrons that diffuse close to the collector-base junction will be swept across that junction (if the collector-base junction is reverse biased), because the field is such that it 'attracts' electrons from base to collector. These electrons form collector current.

Thus there are two significant components of base current -- holes injected from B to E, and holes to recombine with some of the electrons injected from emitter to base (there is a negligible additional component of reverse collector-base leakage). While not equal, these values are generally similar (recombination current is usually lower than injection current). 

Emitter current consists of holes recombining and electrons injected. Because of the structure of the junction, the injection component dominates.

Collector current is primarily the injected emitter electron current, minus some small amount that is lost due to recombination.

So, because a) at the B-E junction electron injection is greater than hole injection, and b) electron recombination in the base is small, the collector current is a large (say 99 %) fraction of the emitter current -- therefore the base current (which is the difference) is about 1 % of the emitter current. 

These parameters differ from device to device, with temperature, and with some imperfections and other defects in devices, but the basic principles are consistent.