TLDR: Probability of being on same route as [Raikou, Entei] using each of the following paths after releasing the roamers:

Burned tower B1 -> Ecruteak -> Route 37
[0.074172, 0.255767]
Burned tower B1 -> Ecruteak -> West gate -> Route 38
[0.186696, 0.214645]
Burned tower B1 -> Ecruteak -> East gate -> Route 42 (Impossible without randomizing key items)
[0.127219, 0.175284]

Note that these odds assume that you use an escape rope to leave the basement. If you use the steps, there will be an additional map transition and your odds will generally be worse:

Burned tower B1 -> Burned tower F1 -> Ecruteak -> Route 37
[0.131471, 0.057051]
Burned tower B1 -> Burned Tower F1 -> Ecruteak -> West gate -> Route 38
[0.105744, 0.093397]
Burned tower B1 -> Burned Tower F1 -> Ecruteak -> East gate -> Route 42 (Impossible without randomizing key items)
[0.208236, 0.13929]

Python script to calculate odds: https://hastebin.com/abaqamajes.py

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When releasing the roamers, Raikou will always start at route 42 and Entei will always start at route 37. Every time the player moves to a new map, all roamers will update position as follows:

- With 1/8 chance, jump to a completely random route that the player is not in.
- Choose a random number n from 1 to 4. If n is greater than the number of possible next routes, try again from the beginning.
- The next route will be the nth route in the list of possible next routes unless the player just left that route. If this is the case, try again from the beginning.

If the player uses Fly or loads a save, all roamers will jump to a completely random route. 

Possible next routes from current route can be found below. For example, from Entei's starting route of 37, Entei can go to routes 36, 38, and 42.
  29: [30, 46]
  30: [29, 31]
  31: [30, 32, 36]
  32: [36, 31, 33]
  33: [32, 34]
  34: [33, 35]
  35: [34, 36]
  36: [35, 31, 32, 37]
  37: [36, 38, 42]
  38: [37, 39, 42]
  39: [38]
  42: [43, 44, 37, 38]
  43: [42, 44]
  44: [42, 43, 45]
  45: [44, 46]
  46: [45, 29]

Source: https://github.com/pret/pokecrystal/blob/2fe0cbbb19df504723934f39473064033c64ef6f/engine/overworld/wildmons.asm#L642-L664